求解二维热传导方程的一个高精度显格式

A High-Order Accuracy Explicit Difference Scheme for Solving 2-D Heat Conduction Equation

利用待定系数法提出了求解二维热传导方程的一个三层高精度显式差分格式,格式的截断误差达到了O(Δt^(3)+Δx^(4)),通过Fourier分析法证明了当r<1/6时,格式是稳定的,最后通过数值实验,说明差分格式是有效的,且理论分析与实际计算相吻合.

In the paper, a three-level explicit difference scheme with high accuracy for solving two-dimension heat conduction equation by the method of undetermined parameters was proposed. The truncation error of the scheme was O(Δt^(3)+Δx^(4)). The difference scheme was proved to be stable if r<1/6 by Fourier method. Finally, the numerical experiment showed that the difference scheme was effective, and theoretical analysis is consistent with the practical calculation.