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In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to consider a discrete data assimilation algorithm for the three dimensional planetary geostrophic equations of large-scale ocean circulation in the case that the observable measurements, obtained discretely in time, may be contaminated by systematic errors, which works for a general class of observable measurements, such as low Fourier modes and local spatial averages over finite volume elements. We will provide some suitable conditions to establish asymptotic in time estimates of the difference between the approximating solution and the unknown exact (reference) solution in some appropriate norms for these two different kinds of interpolation operators, which also shows that the approximation solution of the proposed discrete data assimilation algorithm will convergent to the unique unknown exact (reference) solution of the original system at an exponential rate, asymptotically in time if the observational measurements are free of error. [ABSTRACT FROM AUTHOR]

In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational properties of the sparsity set, along with differentiation properties of the objective function in the SLS model, the first-order optimality conditions are analysed in terms of the stationary points. Based on the equivalent characterization of the stationary points, we propose the Newton Hard-Threshold Pursuit (NHTP) algorithm and establish its locally quadratic convergence under some regularity conditions. Numerical experiments conducted on simulated datasets including cases of Completely Positive(CP)-tensors and symmetric strong M-tensors illustrate the efficiency of our proposed NHTP method. [ABSTRACT FROM AUTHOR]

In this paper, we considered the existence of ground state solutions to the following Choquard equation { − Δ u = λ u + (I α ∗ F (u)) f (u) + μ | u | q − 2 u in R N , ∫ R N | u | 2 d x = a > 0 , where N ≥ 3 , I α is the Riesz potential of order α ∈ (0 , N) , 2 < q ≤ 2 + 4 N , μ > 0 and λ ∈ R is a Lagrange multiplier. Under general assumptions on F ∈ C 1 (R , R) , for a L 2 -subcritical and L 2 -critical of perturbation μ | u | q − 2 u , we established several existence or nonexistence results about the normalized ground state solutions. [ABSTRACT FROM AUTHOR]

In this paper, we establish some necessary and sufficient conditions for the solvability to a system of two-sided Sylvester-like tensor equations over the quaternion algebra. We also construct an expression of the general solution to the system when it is solvable. As an application, we give some solvability conditions and expressions of the η -Hermitian solutions to some systems of two-sided Sylvester-like quaternion tensor equations. We also provide some algorithms and numerical examples to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) target localization by using hybrid time difference of arrival (TDOA) and angle of arrival (AOA) measurements from multiple sensors has been an active research area for several decades due to its extensive applications in various fields. For this nonlinear estimation problem, the pseudolinear system of equations constructed by using the measurements generally acts as the basis of numerous localization algorithms. In this paper, we aim to improve the performance of 3D TDOA–AOA localization by introducing the constrained total least squares (CTLS) framework wherein the inherent characteristics of the pseudolinear equations can be properly taken into consideration. On the basis of the total least squares model, the CTLS model for 3D TDOA–AOA localization is established by imposing the inherent characteristics of the pseudolinear equations as additional constraints. Then, the multi-constraint optimization problem in CTLS model is solved by using an iterative algorithm based on successive projections. Extensive numerical simulations are accomplished for evaluating the performance of the proposed CTLS algorithm. The results show that the proposed algorithm gives moderate accuracy enhancement with acceptable computational cost, and more importantly, it is more robust to large measurement noise than the compared algorithms. [ABSTRACT FROM AUTHOR]

This paper examines serial production lines with unreliable non-identical parallel machines at each workstation and intermediate buffers with finite capacities. All machines are assumed to have exponential service times, times to failure and repair times. An efficient decomposition technique is introduced for the performance evaluation of such lines. Rather than replacing each parallel-machine workstation with an equivalent single-server workstation, the main contribution of this paper is the presentation of a direct approach to derive and apply decomposition equations directly for every parallel machine at each workstation. Experimental results indicate that such a method can provide a computationally efficient algorithm to analyse large serial unreliable multi-server production lines with a good accuracy compared against simulation and other available methods. [ABSTRACT FROM AUTHOR]

Structure-preserving doubling algorithms (SDAs) are efficient algorithms for solving Riccati-type matrix equations. However, breakdowns may occur in SDAs. To remedy this drawback, in this paper, we first introduce Ω -symplectic forms (Ω -SFs), consisting of symplectic matrix pairs with a Hermitian parametric matrix Ω. Based on Ω -SFs, we develop modified SDAs (MSDAs) for solving the associated Riccati-type equations. MSDAs generate sequences of symplectic matrix pairs in Ω -SFs and prevent breakdowns by employing a reasonably selected Hermitian matrix Ω. In practical implementations, we show that the Hermitian matrix Ω in MSDAs can be chosen as a real diagonal matrix that can reduce the computational complexity. The numerical results demonstrate a significant improvement in the accuracy of the solutions by MSDAs. [ABSTRACT FROM AUTHOR]

The linear programming problem provided to bipolar fuzzy relation equation constraints is considered in this paper. The structure of bipolar fuzzy relation equation system is studied with the maxproduct composition. Two new concepts, called covering and irredundant covering, are introduced in the bipolar fuzzy relation equation system. A covering-based sufficient condition is proposed to check its consistency. The relation between two concepts is discussed. Some sufficient conditions are presented to specify one of its optimal solutions or some its optimal components based on the concepts. Also, some covering-based sufficient conditions are given for uniqueness of its optimal solution. These conditions enable us to design some procedures for simplification and reduction of the problem. Moreover, a matrixbased branch-and-bound method is presented to solve the reduced problem. The sufficient conditions and algorithm are illustrated by some numerical examples. The algorithm is compared to existing methods. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different constant values of the generalized diffusion coefficient on the algorithms' convergence is analyzed. The convergence rate of the algorithms is analyzed as the fractional order of the time derivative changes. The paper demonstrates that the algorithms exhibit slow superlinear convergence when the fractional order is close to zero, almost finite step convergence (exact finite step convergence for wave case) when the order approaches two, and faster superlinear convergence as the fractional order increases in between. The transitional nature of the algorithms' behavior is effectively captured through estimates with changes in the fractional order, and the results are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications 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.)

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University 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 paper considers a high-order numerical method for a computed solution of multidimensional convection-diffusion-reaction equation with time-fractional derivative subjected to appropriate initial and boundary conditions. The stability and error estimates of the proposed numerical approach are analyzed using the L ∞ (0 , T ; L 2) -norm. The theoretical study suggests that the new technique is unconditionally stable and temporal accurate with order O(τ2+α), where τ denotes the time step and 0 < α < 1. This result shows that the developed algorithm is faster and more efficient than a broad range of numerical techniques widely studied in the literature for the considered problem. Numerical experiments confirm the theory and they indicate that the proposed numerical scheme converges with accuracy O(τ2+α + h4), where h represents the space step. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a second-order partitioned method with multiple-time-step technique for the nonstationary Stokes-Darcy model. This method allows different time steps in different subdomains and improves the accuracy by the time filters. Besides, by designing new error estimate and time step adjustment strategy, we extend this method to variable timestep and develop single and double adaptive algorithms. Constant and variable time step tests are given to confirm the theoretical analysis and illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The information content of the classic equations describing the problem of forced hydraulic jumps in open channels is the subject of this paper. The forcing refers to designed structural composites to transform incoming supercritical flows into outgoing subcritical flows through hydraulic jumps. The complete flow history through such systems is described by two stable flow profiles, which are interlocked and one can jump to the other. The interlocked profiles underpin a hydraulic effect known as hysteresis with the prime feature of the dependence of flows on their past history. The paper develops an algorithm by using classic hydraulic equations alone to identify hysteresis by building on tacit knowledge already published. The algorithm reproduces the effects of catastrophe theory and shows that hysteresis has predictable configurations. It is validated for geometries with step-rises by using published experimental data; as well as a flume with abrupt contractions by authors' experimental data. [ABSTRACT FROM AUTHOR]

Copyright of Przeglad Elektrotechniczny is the property of Przeglad Elektrotechniczny 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 paper is focused on the development and analysis of suboptimal decision algorithms for a collection of robots that assist a remotely located operator in perimeter surveillance. The operator is tasked with the classification of incursions across the perimeter. whenever there is an incursion into the perimeter, an unattended ground sensor (UGS) in the vicinity, signals an alert. A robot services the alert by visiting the alert location, collecting information, e.g., photo and video imagery, and transmitting it to the operator. The accuracy of operator's classification depends on the volume and freshness of information gathered and provided by the robots at locations where incursions occur. There are two competing objectives for a robot: it needs to spend adequate time at an alert location to collect evidence for aiding the operator in accurate classification but it also needs to service other alerts as soon as possible, so that the evidence collected is relevant. The decision problem is to determine the optimal amount of time a robot must spend servicing an alert. The incursions are stochastic and their statistics are assumed to be known. This problem can be posed as a Markov Decision Problem. However, even for two robots and five UGS locations, the number of states is of the order of billions rendering exact dynamic programming methods intractable. Approximate dynamic programming (ADP) via linear programming (LP) provides a way to approximate the value function and derive suboptimal strategies. The novel feature of this paper is the derivation of a tractable lower bound via LP and the construction of a suboptimal policy whose performance improves upon the lower bound. An illustrative perimeter surveillance example corroborates the results derived in this paper. [ABSTRACT FROM AUTHOR]

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A풱−풱‾B=C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, based on the Lagrange multiplier method, we construct a maximum principle preserving scheme for the time-fractional Allen-Cahn equation of 2- α (0 < α < 1) order. The correction energy of this scheme is increased by a term compared to the original energy, which is O (τ α). We prove that our scheme is unconditionally stable related to the corrected energy and verify the convergence, maximum principle, and energy conservation properties of the algorithm through numerical examples. We also find that the larger the α , the faster the evolution of the time-fractional Allen-Cahn equation. [ABSTRACT FROM AUTHOR]

In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on a polyhedral element with arbitrary shape. The key tools are the notion of Tchakaloff discretization set and the solution of moment-matching equations by Lawson-Hanson iterations for NonNegative Least-Squares. Several numerical tests are presented. The method is implemented in Matlab as open-source software. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast Alikhanov algorithm with nonuniform time steps for a two dimensional distributed‐order time–space fractional advection–dispersion equation. First, an efficient fast Alikhanov algorithm on the general nonuniform time steps for the evaluation of Caputo fractional derivative is presented to sharply reduce the computational work and storage, and are applied to the distributed‐order time fractional derivative or multi‐term time fractional derivative under the nonsmooth regularity assumptions. And a generalized discrete fractional Grönwall inequality is extended to multi‐term fractional derivative or distributed‐order fractional derivative for analyzing theoretically our algorithm. Then the stability and convergence of time semi‐discrete scheme are investigated. Furthermore, we derive the corresponding fully discrete scheme by finite element method and discuss its convergence. At last, the given numerical examples adequately confirm the correctness of theoretical analysis and compare the computing effectiveness between the fast algorithm and the direct method. [ABSTRACT FROM AUTHOR]

This paper describes two new iterative algorithms for determining absolute value equations. The algorithms are based on a splitting of the coefficient matrix. Moreover, we analyze the convergence effects of the presented algorithms via some theorems. Eventually, numerical tests are provided to confirm the credibility of our procedures. [ABSTRACT FROM AUTHOR]

Copyright of Rolling Stock (1002-7602) is the property of Rolling Stock 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.)

A modified-upwind with block-centred finite difference scheme on the basis of the two-grid algorithm is presented for the convection-diffusion-reaction equations. This scheme can keep second-order accuracy in spatial mesh sizes for both state variables and fluxes in the convection–diffusion–reaction problem. Moreover, the two-grid algorithm is constructed in order to solve semilinear convection-dominated problems efficiently, in which the main idea is to settle an original semilinear equation on the coarse space, and next to settle a linearized equation on the fine space. The error estimate of the method proposed in this paper is given through theoretical analysis. It is indicated that the two-grid algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O (h 1 / 2). Thus, solving such a large-scale nonlinear problem is as easy as linearized problems. Besides, there are some numerical experiments to corroborate in practice that the algorithm is effective and robust to solve convection–diffusion–reaction problems. [ABSTRACT FROM AUTHOR]

Minimizing total harmonic distortion (THD) with less system complexity and computation time is a stringent constraint for many power systems. The multilevel inverter can have low THD when switching angles are selected at the fundamental frequency. For low-order harmonic minimization, selective harmonic elimination (SHE) is the most adopted and proficient technique but it involves the non-linear transcendental equations which are very difficult to solve analytically and numerically. This paper proposes a genetic algorithm (GA)-based optimization technique to minimize the THD of cascaded H-bridge multilevel inverter. The GA is the finest approach for solving such complex equations by obtaining optimized switching angles. The switching angles are calculated by the genetic algorithm by solving the nonlinear transcendental equations. This paper has modeled and simulated a five-level inverter in MATLAB Simulink. The THD comparison is carried out between step modulation method and optimization method. The results reveal that THD has been reduced from 17.88 to 16.74% while third and fifth harmonics have been reduced from 3.24%, 3.7% to 0.84% and 3.3%, respectively. The optimization method along with LC filter significantly improves the power quality providing a complete sinusoidal signal for varying load. [ABSTRACT FROM AUTHOR]

In this paper, using the real representation method, we study the reduced biquaternion matrix equation A X = B . Taking advantage of the special structure of real representation of reduced biquaternion, we transform the problem of reduced biquaternion matrix into corresponding problem of real matrix. We propose the expressions of the special minimal norm least squares solution of the reduced biquaternion matrix equation A X = B , and the corresponding algorithms only perform real arithmetic. Numerical examples are provided to illustrate that our algorithm are efficient and easily understood. We also apply the minimal norm pure imaginary least squares reduced biquaternion solution to color image restoration. [ABSTRACT FROM AUTHOR]

Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this paper, we firstly discuss the boundedness of a local bi-cubic Lagrange interpolation operator. And then, taking the semilinear parabolic equation as an example, we first construct a variable-step high-order nonlinear difference algorithm using compact difference technique in space and the second-order backward differentiation formula with variable temporal stepsize in time. With the help of discrete orthogonal convolution kernels, temporal-spatial error splitting idea and a cut-off numerical technique, the unique solvability, maximum-norm stability and corresponding error estimate of the high-order nonlinear difference scheme are established under assumption that the temporal stepsize ratio satisfies rk := τk/τk−1 < 4.8645. Then, an efficient two-grid high-order difference algorithm is developed by combining a small-scale variable-step high-order nonlinear difference algorithm on the coarse grid and a large-scale variable-step high-order linearized difference algorithm on the fine grid, in which the constructed piecewise bi-cubic Lagrange interpolation mapping operator is adopted to project the coarse-grid solution to the fine grid. Under the same temporal stepsize ratio restriction rk < 4.8645 on the variable temporal stepsize, unconditional and optimal fourth-order in space and second-order in time maximum-norm error estimates of the two-grid difference scheme is established. Finally, several numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the nonlinear fractional pseudo‐parabolic equations (FPPEs). We propose an accurate numerical algorithm for solving the aforementioned well‐known equation. The problem is discretized in the temporal direction by utilizing a graded mesh linearized scheme and in the spatial direction by the Galerkin‐spectral scheme. We investigate the stability conditions of the proposed scheme. We also provide an H1$$ {H}^1 $$ error estimate of the proposed approach to demonstrate that it is convergent with temporal second‐order accuracy for fitted grading parameters. The proposed scheme is also extended to tackle coupled FPPEs. Numerical experiments are provided to validate the accuracy and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

The paper investigates iterative algorithms for solving the equation according to the Kalendar-Van Dusyn formula, which describes the dependence of the electrical resistance of the Pt100 family sensor on temperature. This family of platinum sensors is considered quasi-linear, but for high-precision measurements the nonlinearity of the sensor cannot be neglected, so it is necessary to solve the nonlinear equation of Pt100. At minus temperatures, the equation according to the Kalendar-Van Dusyn formula reaches the fourth power and has no solution with respect to temperature in an analytical form. The analysis of the previously published iterative algorithm for the approximate solution of the equation reveals a desadvantage of this algorithm. The residual error of the solution is not a monotonic function of the argument, because it contains extrema, moreover, the sign of the error changes to the opposite after each extremum. The purpose of this study was to obtain an algorithm that provides the residual error in the form of a monotonic deterministic function of the argument with the minimization of the maximum error value. The possibility to modify the iterative algorithm-prototype in an elementary way by fixing the number of iterations is shown. The residual error of solving the equation according to the modified algorithm has the form of a monotonic deterministic function of the argument. It is assumed that any iterative calculation algorithm can be improved in this way. At the same time, the minimization of the error values of the modified algorithm is achieved by setting the maximum number of iterations compared to the prototype algorithm. To overcome this desadvantage of the modified algorithm, a new algorithm is proposed, in which, in addition to a fixed number of iterations, the property of the smallness of the components of higher degrees is used. The high efficiency of the new algorithm is shown, which reduces the residual error of the solution to a negligible value in just four iterations. It is claimed that the high efficiency of the new algorithm makes further research in the direction of its improvement unnecessary. The article presents a scheme of the new algorithm and a corresponding program on the VBA platform for Excel, which is suitable for direct use in the software of temperature meters based on Pt100 resistance temperature sensors. References 5, figures 4, tables 3. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of inequalities associated with circular cones. By constructing a new smoothing function, the problem is reformulated as a system of parameterized smooth equations. In addition, we suggest a Newton-type algorithm for solving the smooth equations so that a solution of the problem concerned is found. In particular, the algorithm is proved to be globally and locally quadratically convergent under suitable conditions. The preliminary numerical results demonstrate that the algorithm is effective. [ABSTRACT FROM AUTHOR]

This paper intends to solve the time-varying Yang-Baxter-like matrix equation (TVYBLME), which is frequently employed in the fields of scientific computing and engineering applications. Due to its critical and promising role, several methods have been constructed to generate a high-performing solution for the TVYBLME. However, given the fact that noise is ubiquitous and inevitable in actual systems. It is necessary to design a computational algorithm with strong robustness to solve the TVYBLME, which has rarely been mentioned previously. For this reason, to remedy shortcomings that the conventional computing methods have encountered in a noisy case, a modified Newton integration (MNI) neural algorithm is proposed and employed to solve the TVYBLME. In addition, the related theoretical analyses show that the proposed MNI neural algorithm has the noise-tolerance ability under various noisy cases. Finally, the feasibility and superiority of the proposed MNI neural algorithm to solve the TVYBLME are verified by simulation experiments. [ABSTRACT FROM AUTHOR]

This paper revisits the study of optical solitons that is governed by one of the three forms of derivative nonlinear Schrödinger's equation that is also known as Chen–Lee–Liu model. This model is investigated by the aid of fully shifted Jacobi's collocation method with two independent approaches. The first is discretization of the spatial variable, while the other is discretization of the temporal variable. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model. [ABSTRACT FROM AUTHOR]

This paper is concerned with a numerical spectral solution to a one-dimensional linear telegraph type equation with constant coefficients. An efficient Galerkin algorithm is implemented and analyzed for treating this type of equations. The philosophy of utilization of the Galerkin method is built on picking basis functions that are consistent with the corresponding boundary conditions of the telegraph type equation. A suitable combination of the orthogonal shifted Gegenbauer polynomials is utilized. The proposed method produces systems of especially inverted matrices. Furthermore, the convergence and error analysis of the proposed expansion are investigated. This study was built on assuming that the solution to the problem is separable. The paper ends by checking the applicability and effectiveness of the proposed algorithm by solving some numerical examples. [ABSTRACT FROM AUTHOR]

Copyright of Eastern-European Journal of Enterprise Technologies is the property of PC TECHNOLOGY CENTER 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.)

The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed-integer nonlinear program and, hence, hard to solve. In this paper, we propose a heuristic algorithm that is based on the recently developed convex relaxation of the ac optimal power flow problem. The algorithm is computationally efficient and scales linearly with the number of redundant lines. It requires neither parameter tuning nor initialization for different networks. It successfully computes an optimal configuration on all four networks we have tested. Moreover, we have proved that the algorithm solves the feeder reconfiguration problem optimally under certain conditions for the case where only a single redundant line needs to be opened. We also propose a more computationally efficient algorithm and show that it incurs a loss in optimality of less than 3% on the four test networks. [ABSTRACT FROM PUBLISHER]

In delay-tolerant networks (DTNs), stable end-to-end connections do not always exist. Messages are forwarded, assisted by the mobility of nodes, in a store–carry–forward paradigm. The mobility of nodes in most DTNs has a certain statistical regularity; thus, using historical information in DTNs to compute the delivery quality of nodes can help to select good forwarding nodes. This paper aims to establish a routing scheme based on multihop delivery quality, which is designed to reduce the energy consumption of message forwarding while maintaining a high delivery rate. We characterized the multihop delivery quality of each node with an expected delay and an expected probability, parameterized by the remaining hop count. Based on these two quality metrics, we developed two algorithms, namely, the delay-inferred forwarding (DIF) algorithm and the probability-inferred forwarding (PIF) algorithm. The basic idea of DIF and PIF is to find the optimal forwarding path by minimizing the expected delay and by maximizing the expected probability, respectively, in the hop graph that is defined in this paper. We performed extensive trace-driven simulations to compare our algorithm to other representative routing algorithms using several real traces. We observed the following: 1) Compared with the delegation algorithm, which uses one-hop delivery quality, both DIF and PIF significantly improve the message delivery rate, and they yield more improvements as the mobility of nodes becomes more regular; and 2) compared with the state-of-the-art optimal opportunistic forwarding (OOF) algorithm, which also uses a multihop delivery quality, DIF and PIF have significantly smaller forwarding overhead (with the maximum reduction in the number of forwarding being over 40%), whereas they are quite close to OOF in terms of both delivery rate and average delay. [ABSTRACT FROM PUBLISHER]

Van Genuchten (VG) equation is the most commonly used equation of soil moisture characteristic curve, and the accuracy of its parameters directly affects the calculation accuracy of soil moisture motion equation. In order to obtain the parameters of the equation more accurately, this paper establishes an optimization model of the VG equation parameters. This optimization model uses the advantages of the cuckoo search algorithm and the differential evolution algorithm to combine the two into a new hybrid cuckoo search algorithm, namely DECS algorithm, and uses this algorithm to solve the parameter optimization problem of VG equation of soil moisture characteristic curve. By collecting and analyzing the relevant experimental data of various soil qualities, the dehumidification and moisture absorption curves of three different soil qualities were selected for simulation calculation. The results show that in the experiment of solving the parameter estimation problem of the VG equation, the DECS hybrid algorithm has better exploration and development capabilities than the cuckoo search algorithm. The hybrid algorithm has relatively significant performance in terms of calculation accuracy and convergence. [ABSTRACT FROM AUTHOR]

In this paper, we apply the approximate symmetry transformation group to obtain the approximate symmetry group of the perturbed mKdV-KS equation which is a modified Korteweg-de Vries (mKdV) equation with a higher singularity perturbed term as the Kuramoto-Sivashinsky (KS) equation. Also, an optimal system of one-dimensional subalgebras of symmetry algebra is constructed and the corresponding differential invariants and some approximately invariant solutions of the equation are computed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical treatment of delay reaction-diffusion with the Dirichlet boundary condition. The finite element method with linear B-spline basis functions is utilized to discretize the space variable. The Crank-Nicolson method is used for the processes of time discretization. Sufficient and necessary conditions for the numerical method to be asymptotically stable are investigated. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method. [ABSTRACT FROM AUTHOR]

This paper is devoted to the construction of certain polynomials related to Lucas polynomials, namely, modified Lucas polynomials. The constructed modified Lucas polynomials are utilized as basis functions for the numerical treatment of the linear and non-linear second-order boundary value problems (BVPs) involving some specific important problems such as singular and Bratu-type equations. To derive our proposed algorithms, the operational matrix of derivatives of the modified Lucas polynomials is established by expressing the first-order derivative of these polynomials in terms of their original ones. The convergence analysis of the modified Lucas polynomials is deeply discussed by establishing some inequalities concerned with these modified polynomials. Some numerical experiments accompanied by comparisons with some other articles in the literature are presented to demonstrate the applicability and accuracy of the presented algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the 2D incompressible Navier-Stokes (INS) equations in terms of vorticity and stream function are considered. These equations describe the physics of many phenomena of scientific and engineering. By combining monotone upwind methods and weighted essentially non-oscillatory (WENO) procedures, a new numerical algorithm is proposed to approximate the solution of INS equations. To design this algorithm, after obtaining an optimal polynomial, it is rewritten as a convex combination of second-order modified ENO polynomials. Following the methodology of the traditional WENO procedure, the new non-linear weights are calculated. The performance of the new scheme on a number of numerical examples is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new direct scheme based on Dickson polynomials and collocation points to solve a class of optimal control problems (OCPs) governed by Volterra integro-differential equations namely Volterra integro-OCPs (VI-OCPs). This topic requires to calculating the corresponding operational matrices for expanding the solution of this problem in terms of Dickson polynomials. Further, the highlighted method allows us to transform the VI-OCP into a system of algebraic equations for choosing the coefficients and control parameters optimally. The error estimation of this technique is also investigated which given the high efficiency of the Dickson polynomials to deal with these problems. Finally, some examples are brought to confirm the validity and applicability of this approach in comparison with those obtained from other methods. [ABSTRACT FROM AUTHOR]

In this paper, a new real representation of reduced biquaternion matrix is proposed, and the solutions of the reduced biquaternion matrix equations XF−AX=BY$$ XF- AX= BY $$ and XF−AX˜=BY$$ XF-A\tilde{X}= BY $$ are solved by means of this method. The corresponding numerical algorithm is provided, and the effectiveness of this method is verified by numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical algorithm dealing with multi‐term time‐fractional Burgers‐type equation involving the Caputo derivative. The proposed method consists of temporal discretization of L2$$ L2 $$ formula and spatial discretization using the exponential B‐splines. The semi implicit approach is applied to discretize the nonlinear term u∂xu$$ u{\partial}_{\mathtt{x}}u $$. We adopt the Von–Neumann method to study stability. We also establish the convergence analysis. The proposed method is employed to solve a few numerical examples in order to test its efficiency and accuracy. Comparisons with the recent works confirm the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Przeglad Elektrotechniczny is the property of Przeglad Elektrotechniczny 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 paper, Lie algorithm is used to classify the classical symmetry of a general diffusion-convection equation. The solution process is elucidated for different conditions, and the obtained symmetries can be used to study the solution properties of the diffusion-convection equation. [ABSTRACT FROM AUTHOR]

In this paper, 8 × 8 real matrix representations of elliptic biquaternions are obtained and by means of these representations, a general method is developed to solve the linear elliptic biquaternion equations. Then, this method is applied to the well-known quaternion equations X−QXR = S and QX−XR = S over the elliptic biquaternion algebra. Also, some illustrative numerical examples are given to show how this method works. Moreover, numerical algorithms for the problems considered in this study are provided. Elliptic biquaternion algebra is generalized form of complex quaternion algebra and so real quaternion algebra. Therefore, the results given in this paper generalize and complement some known results from the literature. [ABSTRACT FROM AUTHOR]