二维抛物型方程的高精度分支稳定隐格式

A High Accuracy Implicit Difference Scheme With Branching Stability 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隐式差分格式.格式的截断误差达到O(Δt2+Δx4).证明了当r≥1/6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.

Proposed in the paper was an implicit difference scheme with high accuracy and branching stability for solving two-dimension parabolic equation by the method of undetermined parameters. The truncation error of the scheme was O（Δt^2＋Δx^4）.The difference scheme was proved to be stable if r≥1/6The numerical experiment showed the numerical solutions of difference scheme and the precise solutions were matched and the difference scheme was effective.