二维Volterra-Fredholm型积分方程问题Taylor配置解法及误差分析

Taylor Collocation Solution and Error Analysis for 2-Dimensional Volterra-Fredholm Integral Equations

利用Taylor配置方法,研究二维Volterra-Fredholm型积分方程问题的数值解.即对研究的积分方程问题进行Taylor配置离散,将积分方程问题转化为代数方程进行求解,建立了Taylor逼近解的求解格式,给出了配置解与精确解的误差估计结果以及阐述理论分析的3个数值例子.

An approximate method for solving 2-dimensional Voherra-Fredholm integral equations is presented by Taylor collocation method. That is, the Volterra-Fredholm integral equations are discretized by Taylor collocation method, which are transformed for the algebraic property systems, the format of Taylor collocation method are obtained. The results of error analysis are given between the collocation solution and the exact solution. Moreover, the effectiveness of this method are illustrated by means of 3 numerical examples.