扩散问题边界积分方程的一类新算法

A new Algorithm for Solving Boundary Integral Equations of Diffusion Equations

采用与时间相关的基本解,把扩散方程转化为边界积分方程,在时间推进的过程中,使用一种新的推进方法,该法无需计算低时间层的内点值,便直接得到希望的时刻的解,由于避免计算低层的内点值,从而计算量大为减少。数值例子显示该算法具有精度高、稳定等特点。

By means of the fundamental solution dependent on time, a diffusion equation can be transformed to a boundary integral equation (BIE). This paper presents a new algorithm for solving BIE of one-dimensional diffusion equations, by which we shall directly compute approximations at the interior nodes for a given time t=T=n T without computing any interior nodes at t=ix(i<n) by stepwise method. It means that our algorithm possesses high accuracy and low complexities. An example shows this conclusion.