经典MPDE方法的一些推广

摘要

将经典的MPDE(modified partial differential equation)方法推广到二维线性方程及线性方程组.本文主要讨论广义MPDEs的推导与算法，还对其稳定性条件进行了判定.%We generalize classical modified partial differential equation(MPDE) approach into a 2D linear equation and a system of linear equations. The algorithm of deducing generalized MPDEs and the criterion for discriminating stability arediscussed. Our work points out the direction towards which the MPDE approach can be applied in extensive scope.