求解热传导方程的一个高精度格式

A High Accuracy Difference Scheme for Solving Heat-Conducting Equations

用待定系数法构造了求解热传导方程的一个高精度隐式格式.格式的截断误差达到O(τ3+h6).证明了当3/8-185(1/2)40≤r<1/2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.

This paper presents an implicit difference scheme with high accuracy for solving heat-conducting equation by means of undetermined parameters.The truncation error of the scheme is O（τ^3＋h^6）.The difference scheme is proved to be stable if 3/8-√185/40≤r〈1/2.The numerical experiment shows the numerical solutions of difference scheme and the precise solutions are matched and the difference scheme is effective.