求解二维热传导方程的高精度紧致差分方法

On a High-Order Compact Difference Method for Solving the Two-Dimensional Heat Equation

基于Richardson外推法提出了一种数值求解二维热传导方程的高阶紧致差分方法.该方法首先利用时间二阶、空间四阶精度的紧致交替方向隐式(ADI)差分格式在不同尺寸的网格上对原方程进行求解,然后利用Richardson外推技术外推一次,最终得到了二维热传导方程时间四阶、空间六阶精度的数值解,数值实验验证了该方法的高阶精度及有效性.

A high-order compact difference method,which is based on the Richardson extrapolation technique,has been proposed to solve the two-dimensional heat equation.Firstly,numerical results have been obtained on different-size meshes by means of a high order alternating direction implicit（ADI）difference scheme,which is second order accurate in time and fourth order accurate in space.Then,the Richardson extrapolation method has been employed to compute a more accurate solution,which is fourth order accurate in time and sixth order accurate in space.The numerical results are given to demonstrate the high accuracy and effectiveness of the present method.