Numerical analysis for distributed-order differential equations

被引：184

作者：

Diethelm, Kai ^{[1
]}

Ford, Neville J. ^{[2
]}

机构：

[1] GNS Gesell Numer Simulat mbH, D-38114 Braunschweig, Germany

[2] Univ Chester, Dept Math, Chester CH1 4BJ, Cheshire, England

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 225卷 / 01期

关键词：

Distributed-order differential equation; Multi-term fractional differential equation; Numerical solution; Convergence; VOLTERRA INTEGRAL-EQUATIONS;

D O I：

10.1016/j.cam.2008.07.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form integral(m)(0) A(r. D(*)(r)u(t))dr = f(t) where in is a positive real number and where the derivative D-*(r) taken to be a fractional derivative of Caputo type of order r. We give a convergence theory for our method and conclude with some numerical examples. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：96 / 104

页数：9

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