西北师范大学学报（自然科学版）2016，Vol.52Issue(2)：13-17,5.DOI:10.16783/j.cnki.nwnuz.2016.02.004
分数阶弱奇异积分微分方程的多项式数值解法
Polynomial method for solving the numerical solution of fractional order integro-differential equation with weakly singular kernel
摘要
Abstract
In order to obtain the numerical solution of fractional order variable coefficients Volterra‐Fredholm integro‐differential equation with weakly singular kernels , an operational matrix method is presented in this paper .An approximate formula which solves solution of arbitrary order weakly singular integral is given by using the definition of Legendre polynomial and some properties . And an operational matrix of fractional derivatives of Legendre polynomial is also obtained . Then the original problem of the equation is changed into a system of algebraic equation through simplifying and descreting the fractional integro‐differential equation . The convergence analysis proves that the method is convergent . The numerical examples show that the approach is effective .关键词
分数阶微分/弱奇异/积分微分方程/Legendre多项式/算子矩阵/数值解Key words
fractional derivative/weakly singular/integro-differential equation/Legendre polynomial/operational matrix/numerical solution分类
数理科学引用本文复制引用
李志文,尹建华,耿万海..分数阶弱奇异积分微分方程的多项式数值解法[J].西北师范大学学报（自然科学版）,2016,52(2):13-17,5.基金项目
国家自然科学基金资助项目 （）
