A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line

Numerical Algorithm for Nonlinear Delayed Differential Systems of nnth Order

The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional and time varying delays. The algorithm is based on combination of the method of steps and the differential transformation. Convergence analysis of the presented method is given as well. Applicability of the presented approach is demonstrated in two examples: A system of pantograph type differential equations and a system of neutral functional differential equations with all three types of delays considered. Accuracy of the results is compared to results obtained by the Laplace decomposition algorithm, the residual power series method and Matlab package DDENSD. Comparison of computing time is done too, showing reliability and efficiency of the proposed technique.Comment: arXiv admin note: text overlap with arXiv:1501.00411 Author's reply: the text overlap may be caused by the fact that this article is concerning systems of equations, while the other paper was about single equation

A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations

The shifted Jacobi-Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm

A matrix method based on the Fibonacci polynomials to the generalized pantograph equations with functional arguments

In this study, a collocation method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method.Comment: 9 Pages, 3 Table

On solving fuzzy delay differential equation using bezier curves

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem

A new numerical method to solve pantograph delay differential equations with convergence analysis

Abstract The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem into a continuous-time optimization problem and then utilize a transferred Legendre pseudospectral method to discretize the problem. By solving this discrete problem, we can attain the pointwise and continuous estimated solutions for the major pantograph delay differential equation. The convergence of method has been considered. Also, numerical experiments are described to show the performance and precision of the presented technique. Moreover, the obtained results are compared with those from other techniques