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The Approximation Solutions for Higher Dimensional Integro-Differential Equations

Authors
  • Chen, Lüping1
  • 1 Xiamen University, School of Mathematical Sciences, Xiamen, 361005, China , Xiamen (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jul 10, 2019
Volume
39
Issue
5
Pages
1309–1318
Identifiers
DOI: 10.1007/s10473-019-0509-7
Source
Springer Nature
Keywords
License
Yellow

Abstract

This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes.

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