积分微分方程组非局部边值问题的再生核数值方法

Reproducing Kernel Numerical Method for Nonlocal Boundary Value Problem for Systems of Integro-differential Equations

提出一种新的解决积分微分方程组非局部边值问题的再生核数值方法.该方法的主要思想是通过在再生核空间中构造一组勒让德多尺度正交基去近似逼近原方程组的解.在定义ε-近似解的基础上,结合配置法获得了积分微分方程组非局部边值问题的近似解,并给出该方法的收敛性和误差估计.数值实验的结果证明了文章方法是有效的.

In this paper,a new reproducing kernel numerical method for solving nonlocal boundary value problem for systems of integro-differential equations is presented.The main idea of this method is to approximate the solution of the mentioned systems of equations by constructing a set of Legendre wavelet bases in the reproducing kernel space.On the basis of defining theε-approximate solution,combined with the collocation method,the approximate solution of systems of integro-differential equations with nonlocal boundary value is obtained.The convergence of this method and the error estimation are given.The results of numerical experiments show that the method is effective.