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In this paper, the one- and two-dimensional stochastic multi-order fractional diffusion-wave equations are introduced and a collocation procedure based on the shifted Jacobi polynomials is established to find their numerical solutions. Through this way, some operational matrices regarding classical and stochastic integrals as well as fractional and classical differentiations of these polynomials, are obtained. By representing the problem solution using an expansion of these polynomials (in which the coefficients of the expansion are unknown) and substituting it into the first problem, as well as by employing the obtained operational matrices, a system containing algebraic equations is obtained. Eventually, the coefficients of expansion and subsequently the solution of the original problem are found by solving this system. The correctness of the procedure is studied by solving four examples. [ABSTRACT FROM AUTHOR]

In this paper, a new numerical method for solving fractional optimal control problems by using hybrid functions is presented. The Riemann–Liouville fractional integral operator for hybrid functions is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. The method is computationally very attractive and gives very accurate results. [ABSTRACT FROM AUTHOR]

Background and Objective: Previous studies suggest a correlation of central venous pressure (CVP) and peripheral venous pressure (PVP) in different surgeries. CVP is one of essential monitoring during coronary arterial bypass graft (CABG). Canulation of peripheral venous catheter and PVP measurement is easier, whit less complication. This study was done to compare the central venous and peripheral venous pressures in the antecubital region in coronary arterial bypass graft surgery. Materials and Methods: This descriptive analytical study was done on 84 patients with American society of anesthesiology III with CABG surgery in Shafa hospital, Kerman, Iran during 2007. The technique of anesthesia was the same in all patients. CVP and PVP were measured every 20 minutes intervals before, on and after cardio-pulmonary pump. Data were analyzed using STAT-10, ANOVA and linear regression tests. Results: A total of 750 simultaneous measurements of CVP and PVP were recorded in all patients. The mean of CVP before of pump was 6.8±0.9 and the mean of PVP was 8.8±1. The mean difference between CVP and PVP was ±2 mmHg and this difference was significant (P<0.05). The mean of CVP on pump was 3.9±1 and the mean on PVP was 7.6±1. The mean difference of these two changeable was ±3.7 mmHg. This difference was significant (P<0.05). The mean of CVP after of pump was 6.5±1 and the mean of PVP was 8.5±1. The mean difference this two changeable was ±2 mmHg and this difference was significant (P<0.05). Conclusion: PVP and CVP are related with each other on cardio-pulmonary pump even in severe hemodynamic condition. PVP and CVP changes are synchronized and PVP is a helpful clinical alternative for estimation of CVP. [ABSTRACT FROM AUTHOR]

This paper examines a time fractional version of the 2D Fokker-Planck equation involved with the Atangana-Baleanu-Caputo fractional derivative, under the Dirichlet boundary conditions. A fully discretization approach based on the meshless local Petrov-Galerkin method and (3 − β) -order approximation is proposed for this equation. More precisely, we apply the meshless local Petrov-Galerkin method based on the Moving Kriging interpolation to discretize the space domain, and utilize the (3 − β) -order approximation together with the θ -weighted finite difference method to discretize the temporal domain. By implementing this method, we get a solution for the problem by solving a system of algebraic equations. The validity of the method is investigated by solving four examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon rationalized Haar functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique. [Copyright &y& Elsevier]

This paper presents a computational technique for the solution of a class of nonlinear singular boundary value problems arising in physiology. The approach is based on a pseudospectral Legendre method in which Legendre-Gauss-Lobatto nodes are used to construct the Nth degree polynomial interpolation to approximate the solution. The method is easy to implement and yields accurate results. Illustrative examples are included to demonstrate the capability of the proposed method, and a comparison is made with existing methods in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the solution of algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples. [Copyright &y& Elsevier]

This article presents a numerical method for solving nonlinear mixed Volterra-Fredholm integral equations. The method is based on two-dimensional Legendre wavelet approximations. The properties of Legendre wavelets are utilized together with the Gaussian integration method to reduce the mixed integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

A numerical method for finding the solution of linear time-varying differential equations is proposed. The properties of the hybrid functions, which consist of block-pulse functions plus rationalized Haar functions, are presented. The properties of the hybrid functions together with the operational matrices of integration and product are then utilized to reduce the solution of differential equations to the solution of algebraic equations. Examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

In this paper we present a method for finding the solution of time-delay systems using a hybrid function. We present the properties of the hybrid functions, which consist of block-pulse functions plus Taylor series. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

Abstract: The Sinc-Galerkin method is presented for solving nonlinear two-point boundary value problems for second order differential equations. A problem arising from chemical reactor theory is then considered. Properties of the Sinc-Galerkin method are utilized to reduce the computation of nonlinear two-point boundary value problems to some algebraic equations. The method is computationally attractive and applications are demonstrated through an illustrative example. [Copyright &y& Elsevier]

A direct method for solving variational problems using single-term Walsh series is presented. Two nonlinear examples are considered. In the first example the classical brachistochrone problem is examined, and in the second example a higher-order nonlinear problem is considered. The properties of single-term Walsh series are given and are utilized to reduce the calculus of variations problems to the solution of algebraic equations. The method is general, easy to implement and yields accurate results. [ABSTRACT FROM AUTHOR]

A numerical method for solving time varying linear quadratic optimal control problems with inequality constraints is presented. The method is based upon hybrid functions approximations. The properties of hybrid functions consisting of block-pulse functions and Legendre polynomials are presented. The operational matrices of integration and product are then utilized to reduce the optimal control problem to the solution of algebraic equations. The inequality constraints are first converted to a system of algebraic equalities. Illustrative examples are included to demonstrate the validity and applicability of the technique. [Copyright &y& Elsevier]

Proposes a numerical method for solving the Gel'fand-Levitan integral equation and an alternative method for the construction of smooth dielectric profiles. Two examples given to demonstrate the accuracy of the proposed method.

The article presents a case study of a 30-year-old man diagnosed with schizophrenia who came to the emergency room after an attempted suicide by penile amputation with a razor blade. The amputated part was aligned with the stump in as natural position as possible with each corpus cavernosum anastomosed using interrupted 3-0 vicryl catgut sutures. The article discusses the penile reimplantation of an amputated penis.

In this research, by utilizing the concept of the mixed Caputo fractional derivative and left-sided mixed Riemann–Liouville fractional integral, we approximate the solution of generalized fractional Benjamin–Bona–Mahony–Burgers equations (GF-BBMBEs). In addition, using Genocchi polynomial properties, we obtain a new formula to approximate the functions by Genocchi polynomials. In the process of computation, we discuss a method of obtaining the operational matrix of integration and pseudo-operational matrices of the fractional order of derivative. Also, an algorithm of obtaining the mixed fractional integral operational matrix is presented. Using the collocation method and matrices introduced, the proposed equations are converted to a system of nonlinear algebraic equations with unknown Genocchi coefficients. In addition, we discuss the upper bound of the error for the proposed method. Finally, we examine several problems to demonstrate the validity and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical method for solving fractional optimal control problems (FOCPs). The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon Bernoulli polynomials. The operational matrices of fractional Riemann–Liouville integration and multiplication for Bernoulli polynomials are derived. The error upper bound for the operational matrix of the fractional integration is also given. The properties of Bernoulli polynomials are utilized to reduce the given optimization problems to the system of algebraic equations. By using Newton’s iterative method, this system is solved and the solution of FOCPs are achieved. Illustrative examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

In this paper, a new numerical method for solving fractional differential equations is presented. The fractional derivative is described in the Caputo sense. The method is based upon Bernoulli wavelet approximations. The Bernoulli wavelet is first presented. An operational matrix of fractional order integration is derived and is utilized to reduce the initial and boundary value problems to system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

We present an efficient computational procedure for the solution of bang–bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advantages and disadvantages are illustrated. In order to resolve the need for a priori knowledge about the structure of optimal control and for resolving the sensitivity to an initial guess, a homotopy continuation technique is combined with the adaptive control parametrization method. The present combined method does not require any assumptions on the control structure and the number of switching points. In addition, the switching points are captured accurately; also, efficiency of the method is reported through illustrative examples. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a new numerical method for solving the optimal control of a class of systems described by integro-differential equations with quadratic performance index is presented. This optimization problem plays an important role in describing the dynamics of an elastic aircraft with allowance for non-steady flow past its profile. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the solution of optimization problem to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique. [Copyright &y& Elsevier]