一类具有弱奇异核的偏积分微分方程的Chebyshev小波数值方法（英文）  

Numerical Treatment for a Class of Partial Integro-Differential Equations with a Weakly Singular Kernel Using Chebyshev Wavelets

作　　者：许小勇 周凤英 谢宇 XU Xiaoyong;ZHOU Fengying;XIE Yu(School of Science, East China University of Technology, Nanchang 330013, China)

机构地区：[1]东华理工大学理学院

出　　处：《应用数学》2019年第4期747-766,共20页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11601076);the Science and Technology Project of Jiangxi Provincial Education Department(GJJ170473)

摘　　要：本文提出一种基于第四类Chebyshev小波配置法,求解了一类具有弱奇异核的偏积分微分方程数值解.利用第四类移位Chebyshev多项式,在Riemann-Liouville分数阶积分意义下,导出Chebyshev的分数次积分公式.通过利用分数次积分公式和二维的第四类Chebyshev小波结合配置法,将具有弱奇异核的偏积分微分方程转化为代数方程组求解.给出了第四类Chebyshev小波的收敛性分析.数值例子证明了本文方法的有效性.In this paper, a numerical method based on fourth kind Chebyshev wavelet collocation method is applied for solving a class of partial integro-differential equations (PIDEs) with a weakly singular kernel under three types of boundary conditions. Fractional integral formula of a single Chebyshev wavelet in the Riemann-Liouville sense is derived by means of shifted Chebyshev polynomials of the fourth kind. By implementing fractional integral formula and two-dimensional fourth kind Chebyhev wavelets together with collocation method, PIDEs with a weakly singular kernel are converted into system of algebraic equation. The convergence analysis of two-dimensional fourth kind Chebyhev wavelets is investigated. Some numerical examples are included for demonstrating the efficiency of the proposed method.

关 键 词：偏积分微分方程 弱奇异核 第四类Chebyshev小波 配置法 分数次积分 

分 类 号：O241.8[理学—计算数学]