应用Legendre小波求解非线性分数阶Volterra积分微分方程

吉林大学学报(理学版)

应用Legendre小波求解非线性分数阶Volterra积分微分方程

黄洁, 韩惠丽

宁夏大学数学计算机学院, 银川 750021

收稿日期:2013-10-16 出版日期:2014-07-26 发布日期:2014-09-26
通讯作者: 韩惠丽 E-mail:nxhan@126.com

Numerical Solution of Nonlinear FractionalOrder VolterraIntegroDifferential Equation by Legendre Wavelets

HUANG Jie, HAN Huili

School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received:2013-10-16 Online:2014-07-26 Published:2014-09-26
Contact: HAN Huili E-mail:nxhan@126.com

摘要/Abstract

摘要：

先利用Legendre小波的分数阶积分算子矩阵将非线性分数阶Volterra积分微分方程转化为非线性代数方程组, 再通过数值求解方程组得到原方程的数值解, 证明了误差边界值, 并用算例验证了该方法的有效性和精确性.

关键词: Volterra积分微分方程, Legendre小波, 分数阶微积分, 块脉冲函数

Abstract:

Nonlinear fractionalorder Volterra integrodifferential equation was transformed into a system of algebraic equations by Legendre wavelet operational matrix of fractional integration. Numerical solution of original equation was obtained through solving algebraic equations and error bound value was estimated. Finally some examples demonstrate the validity and precision of this method.

Key words: Volterra integrodifferential equation, Legendre wavelet, fractional calculus, block pulse function

中图分类号:

O175.6

黄洁, 韩惠丽. 应用Legendre小波求解非线性分数阶Volterra积分微分方程[J]. 吉林大学学报(理学版), 2014, 52(04): 655-660.

HUANG Jie, HAN Huili. Numerical Solution of Nonlinear FractionalOrder VolterraIntegroDifferential Equation by Legendre Wavelets[J]. Journal of Jilin University Science Edition, 2014, 52(04): 655-660.

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