Search

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an op- erational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black- Scholes model. [ABSTRACT FROM AUTHOR]

The XY model is a simplified insulation model for transformers that aims to connect the frequency spectrum of major insulation, insulation paper, and oil. It enables the calculation of the paper's frequency spectrum, facilitating a quantitative evaluation of the transformer's insulation status. Given the scarcity of research addressing the accuracy of the XY model and its corresponding equivalent circuit, this paper investigates the accuracy of the XY model and conducts an in‐depth analysis of the error associated with its equivalent circuit. Firstly, the frequency spectrum of oil‐paper insulations based on the XY model with varying moisture content and structure configurations were measured, followed by the simulation of both the corresponding 2D‐coaxial and XY models. By comparing the results obtained from these simulations with experimental data on oil‐paper insulation, the accuracy of XY model is verified. Subsequently, two variants of the equivalent circuit of the XY model are derived by combining the oil, spacer, and paper differently, which denoted as Type I and II circuits. Finally, we analyzed and explained the errors present in these equivalent circuits compared with the XY model. Our findings show that the width‐thickness ratio of oil‐paper insulation is the most critical influencing factor, while moisture content and insulation structure have a less decisive impact. Notably, for general transformers, as the width‐thickness ratio is between 30 and 70, the relative error of the Type I circuit remains consistently below 0.3% across different frequencies. Consequently, the Type I circuit proves to be a more suitable representation of the equivalent circuit for the XY model in the context of general transformers. © 2024 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

This research reports an error analysis of close-range measurements from a Stonex X300 laser scanner in order to address range uncertainty behavior based on indoor experiments under fixed environmental conditions. The analysis includes procedures for estimating the precision and accuracy of the observational errors estimated from the Stonex X300 observations and conducted at intervals of 5 m within a range of 5 to 30 m. The laser 3D point cloud data of the individual scans is analyzed following a roughness analysis prior to the implementation of a Levenberg--Marquardt iterative closest points (LM-ICP) registration. This leads to identifying the level of roughness that was encountered due to the range-finder's limitations in close-ranging as well as measurements that were obtained from extreme incident angle signals. The measurements were processed using a statistical outlier removal (SOR) filter to reduce the noise impact toward a smoother data set. The geometric differences and the RMSE values in the 3D coordinate directions were computed and analyzed, which showed the potential of the Stonex X300 measurements in close-ranging following a careful statistical analysis. It was found that the error differences in the vertical direction had a consistent behavior when the range increased, whereas the errors in the horizontal direction varied. However, it is more common to produce errors in the vertical direction as compared to the horizontal one. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a distributed order time fractional Coronavirus-19 disease transmission involving Caputo-Prabhakar fractional derivative of α order in time t. The Coronavirus 19 disease model has 8 inger dients leading to system of 8 nonlinear ordinary differential equations in this sense. To solve these types of equations, we proposed a numerical method based on the upon Legendre wavelets optimization approximations. In the first stage, by applying the Legendre wavelets optimization functions and Laplace transform an exact formula for the Prabhakar fractional integral operator is derived. Then, we apply this exact formula and the properties of Legendre wavelets optimization functions to change the given equation into a system of algebraic equations. We calculated the approximation optimal solutions of our system applying the Newton's iterative method. The optimal approximate solutions obtained by using the proposed method are considered as the best solutions for the proposed equation. Error analysis is examined to verify the practical efficiency of the proposed method. In the end, for the efficiency and performance of the proposed method, the numerical results are shown in the figure. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective finite element method for the fourth order elliptic eigenvalue problems in a circular domain. First, by using polar coordinates transformation and the orthogonal property of Fourier basis functions, the original problem is turned into a series of equivalent one-dimensional eigenvalue problems. Second, according to the properties of Laplace operator in polar coordinate, we deduce the polar conditions and introduce suitable weighted Sobolev space. Based on the polar conditions and weighted Sobolev space, we establish the weak form and the corresponding discrete form. Third, we prove the error estimates of approximation eigenvalues and eigenvectors by means of the spectral theory of compact operators for each one-dimensional eigenvalue system. Finally, we provide some numerical experiments to show the validity of the algorithm and the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Partially linear additive models (PLAMs) have attracted much attention in the statistical machine learning community due to their interpretability and flexibility in data-driven prediction and inference. Since the performance of PLAMs is closely related to the structure information of linear and nonlinear components, several approaches have been proposed for regression estimation and data-driven structure discovery. However, the existing automatic discovery strategy is limited to the mean regression framework and is usually sensitive to non-Gaussian noises, e.g. skewed noise and heavy-tailed noise. To further improve the robustness of PLAMs, this paper proposes a Robust Partially Linear Trend Filtering (RPLTF) for regression estimation and structure discovery by integrating the mode-induced error metric and the trend filtering-based nonlinear approximation into regularized PLAMs. Besides the computing algorithm of RPLTF, we establish its upper bound on generalization error in theory. Empirical examples are provided to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we derive error estimates for two second-order numerical schemes for solving the viscous Cahn-Hilliard equation with hyperbolic relaxation, one based on the second-order Crank-Nicolson time marching method and the other on the backward differentiation formula. In both schemes, the nonlinear potential is discretized by the Invariant Energy Quadratization (IEQ) method, which employs an auxiliary variable to produce a linear and unconditional energy-stable structure. After assuming some reasonable boundedness and continuity conditions for the nonlinear function, the optimal error estimate is rigorously derived using mathematical induction. Finally, several numerical experiments are carried out to verify the theoretical predictions of the convergence rate and energy stability of the algorithms. [ABSTRACT FROM AUTHOR]

In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results. • A new locally mass conservative finite element method with interior over-penalized enriched Galerkin methods (IOP-EG). • A priori error analysis of IOP-EG independent of over-penalization. • A robust preconditioner construction and analysis by operator preconditioning approach. [ABSTRACT FROM AUTHOR]

We conduct a rigorous error analysis of the spectral-Galerkin methods for the 1D-1V Vlasov–Poisson system with the velocity variable in both finite and infinite domains. The estimates significantly improve the very limited existing results. We also provide numerical results to demonstrate the effectiveness of the analysed methods. [ABSTRACT FROM AUTHOR]

Approximate adders are some of the fundamental arithmetic operators that are being employed in error-resilient applications, to achieve performance/energy/area gains. This improvement usually comes at the cost of some accuracy and, therefore, requires prior error analysis, to select an approximate adder variant that provides acceptable accuracy. Most of the state-of-the-art error analysis techniques for approximate adders assume input bits and operands to be independent of one another, while some also assume the operands to be uniformly distributed. In this paper, we analyze the impact of these assumptions on the accuracy of error estimation techniques, and we highlight the need to address these assumptions, to achieve better and more realistic quality estimates. Based on our analysis, we propose DAEM, a data- and application-aware error analysis methodology for approximate adders. Unlike existing error analysis models, we neither assume the adder operands to be uniformly distributed nor assume them to be independent. Specifically, we use 2D joint input probability mass functions (PMFs), populated using sample data, in order to incorporate the data and application knowledge in the analysis. These 2D joint input PMFs, along with 2D error maps of approximate adders, are used to estimate the error PMF of an adder network. The error PMF is then utilized to compute different error measures, such as the mean squared error (MSE) and mean error distance (MED). We evaluate the proposed error analysis methodology on audio and video processing applications, and we demonstrate that our methodology provides error estimates having a better correlation with the simulation results, as compared to the state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low regularity. In particular, it is able to handle initial data in Hs for 0 < s ≤ 1. The key feature of the integrator is its ability to distinguish between low and medium frequencies in the solution and to treat them differently in the discretization. This new approach requires a well-balanced filtering procedure which is carried out in Fourier space. The convergence analysis of the proposed scheme is based on discrete (in time) Bourgain space estimates which we introduce in this paper. A numerical experiment illustrates the superiority of the new integrator over standard schemes for rough initial data. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Southeast University (English Edition) is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters; then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented; finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material. [ABSTRACT FROM AUTHOR]

The error analysis of the robot has a very practical significance for improving its accuracy. Therefore, this paper conducts an error analysis for a new five-degree-of-freedom hybrid robot designed to conduct responsible surface machining. Initially, the error sources of the hybrid robot were sorted out to determine the number of error sources. Then, the error mapping model of the hybrid robot is established by the closed-loop vector method and the first-order perturbation method. Based on the mapping property of the 6th-order velocity Jacobi matrix, the compensable and non-compensable error sources affecting the posture error at the end of the hybrid robot are separated. Finally, the error analysis of the separated error sources is carried out to study the effect of single error sources and multiple error sources coupled with the posture error at the end of the robot. The results show that among the individual error sources, the dynamic and fixed platform hinge position error has the most significant effect on the end of the robot; among the integrated posture errors after coupling multiple error sources, the position of the dynamic and fixed platform hinge position error and the translational joint initial position dominate; the analysis of the different trajectories also yields that the error introduced by each error source increases gradually with the increase of the end trajectory. When designing this hybrid robot, attention should be paid to the manufacturing and installation accuracy of the dynamic and fixed platform hinge point positions and the translational joint initial position. [ABSTRACT FROM AUTHOR]

Copyright of China Sciencepaper is the property of China Sciencepaper and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present the first a priori error analysis of a class of space-discretizations by Hybridizable Discontinuous Galerkin (HDG) methods for the time-dependent Maxwell's equations introduced in Sánchez et al. [Comput. Methods Appl. Mech. Eng. 396 (2022) 114969]. The distinctive feature of these discretizations is that they display a discrete version of the Hamiltonian structure of the original Maxwell's equations. This is why they are called ''Hamiltonian" HDG methods. Because of this, when combined with symplectic time-marching methods, the resulting methods display an energy that does not drift in time. We provide a single analysis for several of these methods by exploiting the fact that they only differ by the choice of the approximation spaces and the stabilization functions. We also introduce a new way of discretizing the static Maxwell's equations in order to define the initial condition in a manner consistent with our technique of analysis. Finally, we present numerical tests to validate our theoretical orders of convergence and to explore the convergence properties of the method in situations not covered by our analysis. [ABSTRACT FROM AUTHOR]

Error Analysis was developed by early Second Language Acquisition (SLA) researchers as a way to investigate interlanguage and better understand the second-language learning processes. While it is no longer an active branch of research in SLA, it remains a useful tool for those concerned with accuracy in language use. Given the elevated importance of accuracy in English for Research and Publication Purposes (ERPP), this may be one area where Error Analysis may continue to inform research and praxis. The high degree of language precision demanded in ERPP contexts can be a source of frustration for many engaged in scholarly publication, especially those for whom English is an additional language, such as the Japanese scientists studied in this paper. For Japanese scientists and possibly others, an empirical profile of their most frequent error patterns may help them to better deal with accuracy in research writing. With this motivation, this study applies a corpus-assisted error analysis framework to quantify sentence-level grammar errors and identify the most frequent error patterns in the research article manuscripts of Japanese scientists. A corpus of 53 research article manuscripts with 4,495 errors comprises the primary data. Additionally, two raters and a comparison of errors from scientists from six different L1 backgrounds are employed to triangulate the data and investigate the reliability and generalizability of the findings. Findings reveal that the top ten most frequent errors comprise 52.9%, or half of all errors in the corpus, and are dominated by errors with determiners and prepositions. [ABSTRACT FROM AUTHOR]

In this paper, we describe a spectral Tau approach for approximating the solutions of a system of multi-order fractional differential equations which resulted from coronavirus disease mathematical modeling (COVID-19). The non-singular fractional derivative with a Mittag-Leffler kernel serves as the foundation for the fractional derivatives. Also the operational matrix of fractional differentiation on the domain [0, a] is presented. Then, the convergence analysis of the proposed approximate approach is established and the error bounds are determined in a weighted L² norm. Finally, by applying the Tau method, some of the important parameters in the model's impact on the dynamics of the disease are graphically displayed for various values of the non-integer order of the ABC-derivative. [ABSTRACT FROM AUTHOR]

Copyright of Formación Universitaria is the property of Centro de Informacion Tecnologica (CIT) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, firstly, the residual method, which was developed for initial value problems, is improved to find unknown coefficients without requiring for any system solution. Later, the adaptation of improved residual method is given to find approximate solutions of boundary value problems. Finally, the method improved and adapted for boundary value problems is used to find both critical eigenvalue and eigenfunctions of the one-dimensional Bratu problem. The most significant advantage of the method is finding approximate solutions of nonlinear problems without any linearization or solving any system of equations. Error analysis of the adapted method is given and an upper bound on the approximation error is derived for the eigenfunctions. The numerical results obtained are compared with the theoretical findings. Comparisons and theoretical observations show that the improved and adapted method is very convenient and successful in solving boundary value problems and eigenvalue problems approximately with high accuracy. [ABSTRACT FROM AUTHOR]

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called the Mittag-Leffler–Galerkin method—comprises the finite Mittag-Leffler function and the Galerkin method. The error analysis of the method was studied. As a result, we present two theorems by which the error can be bounded. In addition to error analysis, the residual correction method, which allows us to estimate the error and obtain new approximate solutions, is also presented. To show how the method is applied, and the efficiency of the proposed method, some test examples were considered. When the numerical results obtained were examined, it was found that while the method achieves better results than some of the known methods in the literature, it also achieves results that are similar to those of others of the known methods. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the criteria used to identify mathematics difficulties and the coding processes varied; (b) the mathematics topics investigated encompassed fractions (including fraction computation and representation), problem-solving, and general computation; and (c) a variety of common error types were identified across these mathematical domains. Implications for practitioners and researchers were discussed. [ABSTRACT FROM AUTHOR]

In this work, we present first- and second-order energy-stable linear schemes for the Swift-Hohenberg equation based on first-order backward Euler and Crank-Nicolson schemes, respectively. We prove rigorously that the schemes satisfy the energy dissipation property. We also derive the error analysis for our schemes. Moreover, we adopt a spectral-Galerkin approximation for the spatial variables and establish error estimates for the fully discrete second-order Crank-Nicolson scheme. Numerical results are presented to validate our theoretical analysis. [ABSTRACT FROM AUTHOR]

Numerical methods have essential role to approximate the solutions of Partial Differential Equations (PDEs). Spectral method is one of the best numerical methods of exponential order with high convergence rate to solve PDEs. In recent decades the Chebyshev Spectral Collocation (CSC) method has been used to approximate solutions of linear PDEs. In this paper, by using linear algebra operators, we implement Kronecker Chebyshev Spectral Collocation (KCSC) method for n-order linear PDEs. By statistical tools, we obtain that the Run times of KCSC method has polynomial growth, but the Run times of CSC method has exponential growth. Moreover, error upper bounds of KCSC and CSC methods are compared. [ABSTRACT FROM AUTHOR]

We estimate a function f with N independent observations by using Legendre wavelets operational matrices. The function f is approximated with the solution of a special minimization problem. We introduce an explicit expression for the penalty term by Legendre wavelets operational matrices. Also, we obtain a new upper bound on the approximation error of a differentiable function f using the partial sums of the Legendre wavelets. The validity and ability of these operational matrices are shown by several examples of real-world problems with some constraints. An accurate approximation of the regression function is obtained by the Legendre wavelets estimator. Furthermore, the proposed estimation is compared with a nonparametric regression algorithm and the capability of this estimation is illustrated. [ABSTRACT FROM AUTHOR]

We propose a penalty method to approximate the boundary condition of the Darcy system. For the penalty variational problem, we establish the well-posedness theorem and prove the optimal error estimates of the penalty in the continuous sense. Moreover, we apply the finite element method using RT0/P0 element to discretize the penalty variational problem. The convergence rate depending on both the penalty parameter and mesh size, as well as the applicability of the discrete scheme, are investigated through several numerical experiments on the cases with smooth/non-smooth and convex/non-convex domains. [ABSTRACT FROM AUTHOR]

A 7-DOF cooperative manipulator was designed and manufactured based on the joint driven by dual motor servo. The geometric error model of the end-effector of the manipulator was established, and the parameter errors were analyzed and synthesized based on the principle of independent action of the original parameter errors. Based on the law of large numbers of mathematical statistics and Monte Carlo method, the sensitivity of influencing factors of the geometric position errors was analyzed by numerical simulation, and the parameter errors which have relatively greater influence on the geometric position errors of the manipulator were found. Through the calculation and analysis of the geometric position errors of the end-effector of the manipulator, it was found that the errors obey the Rayleigh distribution in the workspace of the manipulator. The experimental measurement showed that the repeated positioning error of the manipulator is less than 0.0591mm, and the absolute positioning error obeys Rayleigh distribution significantly. It proved that the double motor servo-driven joint has the characteristics of small return errors and high transmission accuracy, and the error analysis is correct, which provides a theoretical basis for the precision design and application of the manipulator. [ABSTRACT FROM AUTHOR]

This paper discussed an analysis of correspondence especially about the kinds of error made by the staff in replying to emails from the customer. All the data were mostly analyzed based on the theory applied by Dulay, Heidi C, and Marina Burt in their book entitled Language Two (1982) and it was also supported by other theories. They were Error Analysis and Interlanguage written by S. P. Corder (1981), Error Analysis Perspective on Second Language Acquisition written by Richard (1974) and beside the other references about, several supporting references that were considered relevant to the topic were also used in this paper. In conducting this research, the library research was applied and there were three steps for the methodology. They were data collection, data analysis, and data source. The information for this paper came from emails written by Ayuna Silver employees. The data was then gathered by reading carefully and then classified based on the types of errors according to the theory used in this qualitative paper. Based on the findings of the study, it can be concluded that Ayuna Silver’s staff made some mistakes, and the factor that caused the errors. There were omissions, additions, misformations, and misordering errors. Overgeneralization, incomplete application of rules, ignorance of rule restrictions, and false concept hypothesized were the factors that caused errors [ABSTRACT FROM AUTHOR]

In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we are able to propose a variant of the scheme that allows one to take advantage of polygons with many edges (such as those composing Voronoi meshes or generated by agglomeration procedures) in order to yield a more accurate discrete solution. The theoretical results are supported by numerical experiments. [ABSTRACT FROM AUTHOR]

We consider a numerical scheme for the approximation of a system that couples the evolution of a two-dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to forced mean curvature flow. The method uses continuous, piecewise linear finite elements in space and a backward Euler scheme in time. Assuming the existence of a smooth solution, we prove optimal error bounds both in L∞(L²) and in L²(H¹). We present several numerical experiments that confirm our theoretical findings and apply the method in order to simulate diffusion induced grain boundary motion. [ABSTRACT FROM AUTHOR]

In the present work, first of all, a new numerical fractional differentiation formula (called the CF2 formula) to approximate the Caputo-Fabrizio fractional derivative of order a; (0 <α < 1) is developed. It is established by means of the quadratic interpolation approximation using three points (t j-2;y(t j-2)); (t j-1;y(t j-1)), and (t j; y(t j)) on each interval [t j-1; t j] for (j ≥ 2), while the linear interpolation approximation are applied on the first interval [t0; t1]. As a result, the new formula can be formally viewed as a modification of the classical CF1 formula, which is obtained by the piecewise linear approximation for y(t). Both the computational efficiency and numerical accuracy of the new formula is superior to that of the CF1 formula. The coefficients and truncation errors of this formula are discussed in detail. Two test examples show the numerical accuracy of the CF2 formula. The CF1 formula demonstrates that the new CF2 is much more effective and more accurate than the CF1 when solving fractional differential equations. Detailed stability analysis and region stability of the CF2 are also carefully investigated. [ABSTRACT FROM AUTHOR]

The article focuses on an error analysis of the truncated Taylor series expansion method for computing matrix exponential by taking into account both the truncation error and the rounding error. Topics include considered the derived error bound will be useful to determine the order of expansion or computing precision required to attain the prespecified error level.

Several applications of computational science and engineering, including population dynamics, optimal control, and physics, reduce to the study of a system of second-order boundary value problems. To achieve the improved solution of these problems, an efficient numerical method is developed by using spline functions. A non-polynomial cubic spline-based method is proposed for the first time to solve a linear system of second-order differential equations. Convergence and stability of the proposed method are also investigated. A mathematical procedure is described in detail, and several examples are solved with numerical and graphical illustrations. It is shown that our method yields improved results when compared to the results available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we describe a computational model for the simulation of fluidstructure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the finite element immersed boundary method (FE-IBM) to the actual finite element distributed Lagrange multiplier (FEDLM) method. We recall the well-posedness of our formulation at the continuous level in a simplified setting. We describe various time semi-discretizations that provide unconditionally stable schemes. Finally, we report the stability analysis for the finite element space discretization, where some improvements and generalizations of the previous results are obtained. [ABSTRACT FROM AUTHOR]

We construct high-order semidiscrete-in-time, and fully discrete (with Fourier-- Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions and carry out corresponding error analysis. The schemes are of implicit-explicit type based on a scalar auxiliary variable approach. It is shown that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. These uniform bounds enable us to carry out a rigorous error analysis for the schemes up to fifth-order in a unified form and derive global error estimates in l∞ (0, T;H¹)∩l2(0, T;H²) in the two-dimensional case as well as local error estimates in l∞ (0, T;H¹)∩l2(0, T;H²) in the three-dimensional case. We also present numerical results confirming our theoretical convergence rates and demonstrating advantages of higher-order schemes for flows with complex structures in the double shear layer problem. [ABSTRACT FROM AUTHOR]

We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete L²- and H¹-norms for a fully discrete approximation. The theoretical results are confirmed with the help of numerical convergence experiments. We also present numerical simulations for some genus-0 surfaces, including for a non-embedded self-shrinker for mean curvature flow. [ABSTRACT FROM AUTHOR]

In this paper, error analysis of the unstructured mesh Galerkin finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential defined on a finite domain is studied. The finite difference method is used to discretize the Caputo time fractional derivative, while the finite element method using unstructured mesh is used to deal with the Riesz fractional operators in space. Both the stability and convergence analysis of the numerical scheme are constructed. Numerical example is conducted to testify the validity of the proposed method. The conservation of the space fractional Schrödinger equation and the non-conservation of the time fractional Schrödinger equation in quantum mechanical system are achieved. This paper proposes an efficient numerical method as well as its theoretical analysis for the two-dimensional time-space fractional Schrödinger equation with time-independent potentials. [ABSTRACT FROM AUTHOR]

In this paper, the interpolating moving least-squares (IMLS) method is discussed. The interpolating moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data. Then we apply the IMLS method for numerical solution of Volterra-Fredholm integral equations, and finally some examples are given to show the accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

Water flow rate plays an important role in the modeling prediction, fault detection and diagnosis, and performance optimization of the variable water flow air‐conditioning (VWFAC) system. However, flowmeters employed by the system's terminals have not been widely used in engineering applications for the constraints in installation space and high installation and retrofit costs. Therefore, in this study, a terminal flow rate estimation method is proposed for the VWFAC system to reduce the dependency on flowmeters. The water flow rate estimation model is developed based on the flow resistance characteristics inside the air handling unit (AHU) and was trained and verified at the Monitoring and Control Laboratory established in the Dalian University of Technology. The results indicate that the maximum root‐mean‐square error (RMSE) during the training and validation sessions are 0.038 m3/h and 0.028 m3/h, respectively, while the corresponding mean absolute percentage error (MAPE) are below 1.4% and 6.5%, which is acceptable for engineering applications. To improve the flow rate estimation accuracy of the model, water temperature, water flow rate, and pressure difference are suggested to cover a wide varied range during the training session as much as possible. Systematic error is an important index in determining the demands for sensor's accuracy class. According to the results of water flow rate, the systematic errors of the estimates are ranged between 0.51% and 0.76%, only about 1/4 to 1/3 of the measurements systematic errors. Based on the error propagation theory, the water flow rate estimates would be reliable if the systematic error of the pressure measurements does not over twice that of the water flow rate measurements. This flow rate estimation method can be further applied to other thermal engineering systems to bring considerable economic benefits for engineering applications. [ABSTRACT FROM AUTHOR]

This study explored the use of error analysis to support the development of pre-service mathematics teachers' subject-matter knowledge of school mathematics topics. Despite extensive literature revealing that both in-service and preservice mathematics teachers have content knowledge gaps in the mathematics they are expected to teach, there is no consensus on how it can be improved. However, a growing body of literature suggests pre-service mathematics teachers' subject matter knowledge of school mathematics topics should be fully developed by the time they exit the teacher training institution. This suggests that there is a need to ensure that pre-service mathematics teachers engage with school mathematics content in their modules. This study, therefore, explored the extent to which the engagement of pre-service mathematics teachers with error analysis could potentially influence the development of their subject matter knowledge of school mathematics topics, specifically focusing on school geometry concepts. The study was conducted with sixty-one preservice mathematics teachers. Data were collected utilizing written tasks and open-ended questionnaire. The findings showed that pre-service mathematics teachers do have knowledge gaps; however, engaging in error analysis resulted in a gradual development of their subject matter knowledge. Based on the findings the author recommends that a large-scale study be done to explore the effect of error analysis towards the development of pre-service mathematics teachers subject matter knowledge of school mathematics topics as well additional research focusing on different topics. [ABSTRACT FROM AUTHOR]

In the manufacturing process of LED chips, the accuracy of the LED chip visual localization system affects the quality of LED chip production directly. There are many errors that have impacts on positioning system accuracy. Therefore, the identification and compensation of the critical errors is key to efficiently improving the precision of the system. Based on this fact, an error analysis method and an error compensation strategy are proposed in this paper. The first step was to measure the relevant error sources that may affect the localization system. Then error model of localization system was established, and the validity of this error model was verified by comparing simulated and actual positioning results. In addition, the impact factors of each error source on localization system accuracy were obtained using the error transfer theory. According to the error analysis results, an efficient error compensation strategy was proposed, which could compensate the errors in order of impact factors, and judge whether the error compensation method is optimal. Finally, the experimental results proved that the proposed error analysis method was valid and the error compensation strategy could efficiently enhance the positioning accuracy to meet the industrial application requirements. [ABSTRACT FROM AUTHOR]

This paper presents a numerical scheme to address a type of fractional spatial–temporal telegraph equations with variable coefficients by applying the modified fractional Legendre wavelets. Compared with other common Legendre wavelets method, a new fractional Legendre wavelet is constructed. The modified fractional Legendre wavelet has two parameters of t and α, and each variable is expressed as tα. The differential operational matrices of modified fractional Legendre wavelets are established by building the relations between the modified Legendre wavelets and modified polynomials functions. The original differential system is transferred into a linear algebraic system of equations by introducing the modified Legendre wavelet vectors and their fractional differential operational matrices. The obtained system can be easily solved by any mathematical technique and tool. The error analysis theorem of the system is detailed investigated by introducing the variables x and t and the parameters α and β. Several numerical experiments, combined with their error analysis, are provided to authenticate that the proposed method is practicable and efficient. [ABSTRACT FROM AUTHOR]

In this paper we study both the fast computation and the related error analysis of many different finite and infinite oscillatory Bessel transforms. By transforming the Bessel function into Confluent hypergeometric function and using its asymptotic expansion, we develop an efficient approach by the contours in the complex plane, corresponding to the paths of steepest descent. Furthermore, we conduct their error analyses in inverse powers of the frequency ω. The related error analyses show that the precision can be improved by either adding more Gauss-Laguerre nodes or increasing the frequency ω. In particular, the method exhibits the high error order. Meanwhile, we apply the proposed method to some other kinds of oscillatory integrals through some simple changes of variables. Numerical experiments can verify our theoretical analysis. It is also shown that the new algorithms are more efficient than the existing Filon-type method and can achieve the same level of accuracy with the method (the XMX method) proposed in Xu, Milovanović and Xiang [46] by some numerical experiments under the given conditions. A combination of the n 1 -point Gauss-Laguerre quadrature rule and the n 2 -point generalized Gauss-Laguerre quadrature rule are used in the XMX method. However, we only use the Gauss-Laguerre quadrature rule for one time in the established method, which makes the theoretical and error analysis simpler than the XMX method. [ABSTRACT FROM AUTHOR]

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N. [ABSTRACT FROM AUTHOR]

The flat-plate momentum test bench is a widely used experimental device in the verification of the momentum law of fluid mechanics, and its error characteristics are of positive significance for theoretical research and engineering innovation and expansion. The SPH-FEM coupling algorithm and spectrum analysis method are used to calculate and analyze the displacement response and spectrum characteristics of the characteristic points of the sensor under different jet loads. Based on them, the cause, classification, law, scope, influence and control method of the measurement error of the system are discussed and analyzed with the application of the error theory and the lateral effect theory of strain gauges; combined with physical experiments, the relevant analysis methods and conclusions are verified. The results show that the measurement error of the system includes linear error and periodic error. Structural deformation in the direction of jet impact is the main source of linear error; linear error increases with the increase of jet loads. Meanwhile, periodic vibration in non-jet direction is the main cause of periodic error, and the periodic error decreases with the increase of jet loads. [ABSTRACT FROM AUTHOR]

In the present paper, we study a class of linear approximation methods for solving semi‐linear delay‐reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth‐order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated. [ABSTRACT FROM AUTHOR]

In this paper, an accurate numerical approach based on the Wilson wavelets and collocation method together with Kumar and Sloan scheme is proposed to numerical solution of a nonlinear fractional Fredholm–Hammerstein integro-differential equations. The presented method transforms solving such problems into solving systems of nonlinear algebraic equations. Error analysis of the established method is investigated theoretically and numerically. The accuracy of the proposed method is investigated on some numerical examples. The obtained results confirms that the presented method is satisfactory for such problems. [ABSTRACT FROM AUTHOR]

This paper presents a finite length analysis of multi-slot type frameless ALOHA based on a dynamic programming approach. The analysis is exact, but its evaluation is only feasible for moderate number of users due to the computational complexity. The analysis is then extended to derive continuous approximations of its key parameters, which, apart from providing an insight into the decoding process, make it possible to estimate the packet error rate with very low computational complexity. Finally, a feedback scheme is presented in which the slot access scheme is dynamically adapted according to the approximate analysis in order to minimize the packet error rate. The results indicate that the introduction of feedback can substantially improve the performance of frameless ALOHA. [ABSTRACT FROM AUTHOR]