一类半线性椭圆方程的二重网格差分算法

应用二重网格差分算法处理了一类半线性椭圆问题。无需求细网格上的非线性解,对粗网格(可以很粗)上的数值解在细网格上进行几次线性修正即可,且重复算法的最后一步可以按粗网格步长任意阶地逼近细网格上的非线性解。算法提高了计算效率但不降低精度,有数值算例加以验证。

A two-grid algorithm for a finite difference solution of semi-linear elliptic equations

An efficient two-grid algorithm was presented for the approximation of semi-linear elliptic equations using the finite difference method. The solution of a nonlinear system in fine space was reduced to the solution of one small system in coarse space and two linear systems on the fine space. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to last step of the algorithm. The numerical results confirm that the algorithm obtains a decrease in the amount of computing time without sacrificing the order of accuracy of the fine grid solution.