Two-dimensional Euler polynomials solutions of two-dimensional Volterra integral equations of fractional order

被引：10

作者：

Wang, Yifei ^{[1
]}

Huang, Jin ^{[1
]}

Wen, Xiaoxia ^{[1
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2021年 / 163卷 / 163期

基金：

中国国家自然科学基金;

关键词：

Two-dimensional Euler polynomial; Fractional Volterra integral equation; Gauss-Jacobi quadrature; Error analysis;

D O I：

10.1016/j.apnum.2021.01.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proposes a method based on two-dimensional Euler polynomials combined with Gauss-Jacobi quadrature formula. The method is used to solve two-dimensional Volterra integral equations with fractional order weakly singular kernels. Firstly, we prove the existence and uniqueness of the original equation by Gronwall inequality and mathematical induction method. Secondly, we use two-dimensional Euler polynomials to approximate the unknown function of the original equation, and the Gauss-Jacobi quadrature formula is used to approximate the integrals in the original equation. Thirdly, we prove the existence and uniqueness of the solution of approximate equation, and the error analysis of the proposed method is given. Finally, some numerical examples illustrate the efficiency of the method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：77 / 95

页数：19

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