| 微分变换法求解二维非线性Volterra积分微分方程 |
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| 引用本文： | 魏金侠,单锐,刘文,靳飞.微分变换法求解二维非线性Volterra积分微分方程[J].应用数学,2012,25(3):691-696. |
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| 作者姓名： | 魏金侠 单锐 刘文 靳飞 |
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| 作者单位： | 燕山大学理学院,河北秦皇岛,066004 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | Volterra积分微分方程 微分变换法 二维非线性 数值解 |
Differential Transform Method for Solving the Two-dimensional Nonlinear Volterra Integro-differential Equation |
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| WEI Jinxia
,
SHAN Rui
,
LIU Wen
,
JIN Fei.Differential Transform Method for Solving the Two-dimensional Nonlinear Volterra Integro-differential Equation[J].Mathematica Applicata,2012,25(3):691-696. |
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| Authors: | WEI Jinxia SHAN Rui LIU Wen JIN Fei |
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| Affiliation: | (College of Sciences,Yanshan University,Qinhuangdao 066004,China) |
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| Abstract: | In order to get the numerical solution of two-dimensional nonlinear Volterra integro-differential equation,we have given differential transform method (DTM).We can simplify 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. |
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| Keywords: | Volterra integro-differential equation Differential transform method Two-dimensional nonlinear Numerical solution |
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