求解抛物型方程的一个高精度隐格式

A High-Order Accuracy Implicit Difference Scheme for Solving Parabolic Equations

用待定系数法构造了求解抛物型方程的一个高精度隐式格式.格式的截断误差达到O（τ4＋h6）.证明了当r≤1＋11005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 one-dimension parabolic type equations by the method of undetermined coefficients. The truncation error of the scheme is O（τ4＋h6）.The difference scheme is proved to be stable if r≤1＋11005.In a numerical experiment, the numerical solutions of the difference scheme and the precise solutions are matched, and the result shows that the difference scheme is effective,,