Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

• 来源期刊: 理论物理通讯：英文版
• 学科: 数学
• 关键词: 微分差分方程 非线性问题 灵敏度法 解析解 直接求解 问题转化 精确解 近似解
• 年，卷（期）: 2012,（1）
• 页码范围: 5-9
• 页数: 5页
• 分类号: O175.7|O177.91
• 语种: 英文

摘要

In this paper an efficient computational method based on extending the sensitivity approach （SA） is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations （DDEs）, the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach.