利用同伦摄动法的四阶微分方程数值解求解方法
发布时间：2018-11-02 08:15
【摘要】：针对四阶微分方程线性和非线性边界值数值解问题,提出了一种使用同伦摄动法的求解方法.首先,在Caputo意义下描述分数导数算子;然后,确定合适的边界初始条件将方程降为经典方程;最后,使用同伦参数来展开求解.实例计算证明了提出方法的有效性、简单性和可靠性.
[Abstract]:A homotopy perturbation method is proposed for solving the linear and nonlinear boundary value numerical solutions of fourth order differential equations. First, the fractional derivative operator is described in the sense of Caputo; then, the proper boundary initial conditions are determined to reduce the equation to classical equation; finally, the homotopy parameter is used to solve the problem. Examples show that the proposed method is effective, simple and reliable.
【作者单位】： 潍坊科技学院通识学院(计算机系);山西大学计算机工程系;
【基金】：山东省教育科学“十二五”规划“高等教育数学专项”课题(CBS15001)
【分类号】：O241.8
[Abstract]:A homotopy perturbation method is proposed for solving the linear and nonlinear boundary value numerical solutions of fourth order differential equations. First, the fractional derivative operator is described in the sense of Caputo; then, the proper boundary initial conditions are determined to reduce the equation to classical equation; finally, the homotopy parameter is used to solve the problem. Examples show that the proposed method is effective, simple and reliable.
【作者单位】： 潍坊科技学院通识学院(计算机系);山西大学计算机工程系;
【基金】：山东省教育科学“十二五”规划“高等教育数学专项”课题(CBS15001)
【分类号】：O241.8
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