解高维抛物型方程的一个高精度显式差分格式

An Explicit Difference Scheme with High-order Accuracy for Solving High-dimensional Parabolic Equation

构造和研究了五维抛物型方程的高精度显式差分格式.首先给出了含参变量的差分方程,并用待定系数法适当地选取了这些参数的表示式,以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4);其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件;接着确定了高精度显式差分格式的稳定性条件为r<2/5;最后给出了数值例子,数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性.

A high -order accuracy explicit difference scheme for solving three - dimensional parabolic equation was constructed and studied. Firstly, the differential equation with parameters was given. At the same time, in order to make the truncation error order of differential equation as high as possible （reaches to O（△t^2＋△x^4） , the method of undetermined coefficient was used to appropriately select the expression of these parame- ters. Secondly, the stability condition of the scheme derived was given using the Fourier method of stability anal- ysis. Then the stability condition of r 〈 2/5 was got. Finally, a numerical example was given. The numerical re- sults show the advantage of the schemes.