THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

doi:10.1007/s10473-019-0509-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1309-1318.doi: 10.1007/s10473-019-0509-7

THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

陈吕萍

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2018-02-05 修回日期:2019-02-19 出版日期:2019-10-25 发布日期:2019-11-11
作者简介:Lüping CHEN,E-mail:lpchen@xmu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (11771357, 11171277), the Fundamental Research Funds for the Central Universities of Xiamen University (2010121002), the Science Foundation of Fujian province of China (S0850029, 2008J0206).

THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

Lüping CHEN

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2018-02-05 Revised:2019-02-19 Online:2019-10-25 Published:2019-11-11
Supported by:
This work was supported by the National Natural Science Foundation of China (11771357, 11171277), the Fundamental Research Funds for the Central Universities of Xiamen University (2010121002), the Science Foundation of Fujian province of China (S0850029, 2008J0206).

摘要/Abstract

摘要： 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.

关键词: integro-differential equations, polynomial approach, Cauchy formula, bicylinder

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.

Key words: integro-differential equations, polynomial approach, Cauchy formula, bicylinder

中图分类号:

32A26

陈吕萍. THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(5): 1309-1318.

Lüping CHEN. THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(5): 1309-1318.

参考文献

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THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

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