A numerical method for solving systems of higher order linear functional differential equations

Abstract

Abstract:Functional di erential equations have importance in many areas of science such as mathematical physics. These systems are di cult to solve analytically.In this paper we consider the systems of linear functional di erential equations [1][2][3][4][5][6][7][8][9] including the term y(αx + β) and advance-delay in derivatives of y . To obtain the approximate solutions of those systems, we present a matrixcollocation method by using Müntz-Legendre polynomials and the collocation points. For this purpose, to obtain the approximate solutions of those systems, we present a matrix-collocation method by using Müntz-Legendre polynomials and the collocation points. This method transform the problem into a system of linear algebraic equations. The solutions of last system determine unknown coe cients of original problem. Also, an error estimation technique is presented and the approximate solutions are improved by using it. The program of method is written in Matlab and the approximate solutions can be obtained easily. Also some examples are given to illustrate the validity of the method.

A collocation method for differential equations with one‐point Taylor initial conditions

“…[1][2][3][4][5] Some of the recent methods include differential transform methods, [6][7][8][9] spectral Galerkin methods, [10][11][12] wavelet methods, 9,[13][14][15][16][17][18] collocation methods, [19][20][21][22][23][24] Legendre methods, [25][26][27] and some other numerical methods for ordinary differential equations. [28][29][30][31][32][33][34][35][36] We consider the following model problem:…”

“…With the rapid growth of science and industry in the 20th century, the numerical methods that solve differential equations attract much attentions in different new fields . Some of the recent methods include differential transform methods, spectral Galerkin methods, wavelet methods, collocation methods, Legendre methods, and some other numerical methods for ordinary differential equations …”