用两种再生核方法求解一类线性常微分方程初边值问题

Solving the Initial Boundary Value Problem for A Class of Linear Ordinary Differential Equations by Two Reproducing Kernel Methods

再生核方法求解初边值问题的关键是构造再生核,使其满足所考虑问题的齐次边界条件.在此我们通过两种再生核方法求解线性常微分方程的初边值问题.一种方法是将齐次边界条件放入再生核中;另一种方法是将所有初边值条件都放入算子里.本文重点在于比较这两种方法求解微分方程数值解的精确性,通过几个数值算例我们发现,方法Ⅰ的精确度更高,所有数值计算都是通过数学软件mathematic8.0给出.

A key of the reproducing kernel method for initial boundary value problems is the construction of the reproducing kernel and satisfying the homogenous boundary conditions of the considered problems.So we solve linear differential equations with initial boundary value problems by two reproducing kernel methods.One method is put the homogeneous boundary conditions in the reproducing kernel;the other way is put all boundary value conditions into the operator.This paper focuses on comparing the accuracy of the two methods for solving numerical solutions of differential equations.Through several numerical examples,we find that the accuracy of method I is higher,and all numerical calculations are given by the mathematical software mathematic8.0.