同伦摄动法在一类线性积微分方程初值问题中的应用

Application of Homotopy Perturbation Method (HPM) in Initial Problem of A Kind of Linear Integro-Differential Equation

积微分方程定解问题在数学与其他科学领域里有着重要的应用,利用积分,将一类积微分方程定解问题转为与之等价的第二类Fredholm-Volterra积分方程,然后利用同伦摄动方法求解第二类Fredholm-Volterra积分方程,可得积微分方程定解问题的解,最后利用matlab符号计算功能对实例进行计算,验证了同伦摄动法在求解积微分方程定解问题中是有效的。

The definite solution problems of Integro-differential equation have special,JX within the of mathematics other Science research. In this study,we firstly transformed a kind of linear Integro-differential equation definite solution problems into the second Fredholm-Volterra caculus equation by integration. Secondly,the homotopy perturbationan method was adopted to solve the equivalent Fredholm-Volterra caculus equation. Finally,error analysis and illustrative examples were showed to demonstrate the validity and applicability of the technique with the matlab symbol compuation function.