二维抛物型方程的一个新的高精度显式差分格式

A new high-order accurate explicit difference scheme for solving two-dimension parabolic equation

用待定系数法构造了求解二维抛物型方程的高精度分支稳定的显式差分格式.格式的截断误差达到O(Δt2+Δx4).证明了当1/15≤r≤1/9时,差分格式是稳定的.通过数值试验,比较了差分格式的解和精确解的区别,说明了差分格式的有效性.

An explicit difference scheme with high accuracy and branching stability is constructed for solving two-dimension parabolic type equation by the method of undetermined parameters. The truncation error of the scheme is O（△t2＋△x4）. The difference scheme is proved to be stable if 1/15≤r≤1/9. The numerical experiment shows the numerical solutions of difference scheme and the precise solutions are matched and the difference scheme is effective.