Numerical solution of fractional diffusion equation over a long time domain

被引:5
作者
Alavizadeh, S. R. [1 ]
Ghaini, F. M. Maalek [1 ]
机构
[1] Yazd Univ, Fac Math, Yazd, Iran
关键词
Fractional diffusion equation; Shifted Legendre polynomials; Rational Legendre functions; Caputo derivative; APPROXIMATION;
D O I
10.1016/j.amc.2015.04.039
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we propose a method to compute approximate solutions to one dimensional fractional diffusion equation which requires solution for a long time domain. For this, we use a set of shifted Legendre polynomials for the space domain and a set of Legendre rational functions for the time domain. The unknown solution is approximated by using these sets of orthogonal functions with unknown coefficients and the fractional derivative of the approximate solution is represented by an operational matrix, resulting in a linear system with the unknown coefficients. Numerical examples are given to demonstrate the effectiveness of the method. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:240 / 250
页数:11
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