重心有理插值配点法求解非线性分数阶Sobolev方程  

Barycentric Rational Interpolation Collocation Method for Solving Nonlinear Fractional Sobolev Equations

作　　者：赵婉露 王玲 赵凯艳 徐秀娟 龚佃选 李金[3] ZHAO Wanlu;WANG Ling;ZHAO Kaiyan;XU Xiujuan;GONG Dianxuan;LI Jin(College of Science,North China University of Science and Technology,Tangshan Hebei 063210,China;Cyberspace Institute of Advanced Technology,Guangzhou University,Guangzhou Guangdong 510006,China;School of Science,Shandong Jianzhu University,Jinan Shandong 250100,China)

机构地区：[1]华北理工大学理学院,河北唐山063210 [2]广州大学网络空间先进技术研究院,广东广州510006 [3]山东建筑大学理学院,山东济南250100

出　　处：《华北理工大学学报(自然科学版)》2025年第2期94-104,共11页Journal of North China University of Science and Technology:Natural Science Edition

基　　金：山东省自然科学基金(ZR2022MA003):重心插值配点法求解分数阶热传导方程。

摘　　要：应用重心有理插值配点法求解非线性分数阶Sobolev方程。对于方程中的非线性项,采用线性化迭代方法,将其转变为线性项,构造了非线性分数阶Sobolev方程的线性化迭代格式。将分数阶导数部分转化为黎曼积分,并利用高斯求积公式近似计算,通过重心有理插值配点法离散方程,得到了不同迭代格式下方程的矩阵方程。数值算例表明了重心有理插值配点法对于求解不同维数的非线性分数阶Sobolev方程具有有效性和较高的计算精度。The barycentric rational interpolation collocation method was applied to solve the nonlinear fractional Sobolev equations.Specifically,the nonlinear term in the equation was transformed into a linear term by the linearized iterative method.This process was used to construct a linearized iterative scheme for nonlinear fractional Sobolev equations.In addition,the fractional derivative part was converted into Riemann integral,and then approximated by Gaussian quadrature formula.By applying the barycentric rational interpolation collocation method to discretize the equation,the matrix equations corresponding to different iterative schemes were derived.The discrete form and application method of initial conditions and boundary conditions were given.Numerical examples show that the barycentric interpolation collocation method is effective and has high computational accuracy for solving nonlinear fractional Sobolev equations with different dimensions.

关 键 词：重心有理插值配点法 非线性分数阶Sobolev方程 迭代方法 矩阵方程 

分 类 号：O241.82[理学—计算数学]