Laguerre多项式求解分数阶Volterra-Fredholm积分-微分方程
Solving Fractional Volterra-Fredholm Integro-differential Equations with Laguerre Polynomials
李晓洁 1陈豫眉2
作者信息
- 1. 西华师范大学数学与信息学院,四川南充 637009
- 2. 西华师范大学公共数学学院,四川南充 637009
- 折叠
摘要
为求分数阶积分-微分方程的近似解,提出了一种基于Laguerre多项式求解分数阶Volterra-Fredholm积分-微分方程的近似方法.首先,在Caputo分数阶导数意义下,将分数阶积分-微分方程转化为Laguerre多项式空间上的矩阵形式.然后,利用配置点得到矩阵方程组来进行求解.最后,通过数值算例验证了该方法的有效性和准确性.该方法与Bernoulli小波法相比更简单精确.
Abstract
In order to find approximate solutions to fractional integro-differential equations,an approximate method for solving fractional Volterra-Fredholm integro-differential equations based on Laguerre polynomials is proposed.Firstly,in the sense of Caputo fractional derivatives,the fractional integro-differential equations are converted into matrix form on Laguerre polynomial space.Then,the matrix equations are obtained by using the collocation points for solution.Finally,the effectiveness and accuracy of this method are verified through numerical examples.This method is simpler and more accurate than the Bernoulli wavelet method.
关键词
Laguerre多项式/Caputo分数阶导数/分数阶Volterra-Fredholm积分-微分方程/矩阵方程Key words
Laguerre polynomials/Caputo fractional derivatives/fractional Volterra-Fredholm integro-differential equation/matrix equation引用本文复制引用
出版年
2024
NETL
NSTL
万方数据