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

作　　者：李晓洁 陈豫眉 LI Xiaojie;CHEN Yumei(College of Mathematics and Information,China West Normal University,Nanchong 637009,China;College of Mathematics Education,China West Normal University,Nanchong 637009,China)

机构地区：[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

出　　处：《西安文理学院学报(自然科学版)》2024年第3期22-29,共8页Journal of Xi’an University(Natural Science Edition)

基　　金：四川省自然科学基金项目(2023NSFSC0073)

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.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 

分 类 号：O241.82[理学—计算数学]