微分变换法求解二维非线性Volterra积分微分方程  

Differential Transform Method for Solving the Two-dimensional Nonlinear Volterra Integro-differential Equation

作　　者：魏金侠[1] 单锐[1] 刘文[1] 靳飞[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《应用数学》2012年第3期691-696,共6页Mathematica Applicata

基　　金：国家自然科学基金资助项目(50875230);河北省教育厅科学研究计划项目(2009159)

摘　　要：为了解决二维非线性Volterra积分微分方程的求解问题,本文给出微分变换法.利用该方法将方程中的微分部分和积分部分进行变换,这样简化了原方程,进而得到非线性代数方程组,从而将原问题转换为求解非线性代数方程组的解,使得计算更简便.文中最后数值算例说明了该方法的可行性和有效性.In order to get the numerical solution of two-dimensional nonlinear Volterra in- tegro-differential equation,we have given differential transform method （DTM）. We can sim- plify the initial equation by transforming the differential part and integral part,then a system of nonlinear algebraic equations is obtained. The original problem is translated into the problem which solves the solution of the system of nonlinear algebraic equations and computation became convenient. Finally, an example shows the feasibility and validity of the method.

关 键 词：VOLTERRA积分微分方程 微分变换法 二维非线性 数值解 

分 类 号：O241.8[理学—计算数学]