并行解Volterra型积微方程的高精度算法  

A high accuracy methods for solving Volterra-type integro-differential equations in parallel

作　　者：张麟[1] 张洋[1] 吕涛[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2010年第5期957-963,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10671136)

摘　　要：本文讨论了Volterra型积微方程的一种基于Laplace反演的数值方法.作者使用四阶精度的差分格式,并行地求解若干个椭圆方程,对这些椭圆方程求得近似解后,再反演得到高精度积微方程的数值解.This paper presents a numerical method for solving Volterra-type integro-differential equations based on the Laplace inversion transform. By means Laplace transformation the Volterra-type integrodifferential equations become elliptic differential equations with a parametric s, which can be solved by the fourth order finite difference equations for given several parametric variable in parallel. After solving these equations we can get the numerical solutions with high accuracy by the inversion process.

关 键 词：VOLTERRA型积分微分方程 数值反演 差分方法 并行算法 

分 类 号：O241.82[理学—计算数学]