二维半线性抛物方程的二重网格差分算法

Two-grid Difference Algorithms for Two-dimensional Semilinear Parabolic Equation

针对二维半线性抛物方程,本文提出了两种二重网格差分算法,并给出了误差估计。该算法能够在粗网格和细网格上线性地求解半线性问题。若重复算法的最后几步可以按粗网格步长任意阶地逼近细网格上的非线性解。

Two efficient methods with two-grid scheme are presented in this paper for the approximation of semilinear parabolic equations by using the finite difference method. The proposed techniques are based on two different spaces defined, respectively, on a coarse grid and a fine grid. By the two-grid algorithms, the semilinear parabolic problem is solved by the linear method without sacrificing the order of accuracy of the fine grid solution. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to final steps of the algorithms.