二维抛物型方程的高精度显式差分格式
A High-Order Accurate Explicit Difference Scheme for Solving Parabolic Equation of Two-Dimension
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摘要: 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112≤ r≤16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，说明了差分格式的有效性。Abstract: In the paper ,an explicit difference scheme has been proposed with high accuracy and branching stability for solving two‐dimension parabolic type equation by the method of undetermined parameters . T he truncation error of the scheme is O(Δt2 + Δx4 ) .T he difference scheme has been proved to be stable if 112≤ r≤ 16 .T he numerical experiment show s the numerical solutions of difference scheme and the precise solutions are matched and the difference scheme is effective .
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