解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 Parabolic Equation

引入耗散项的方法,构造一个条件稳定的显格式,其稳定性条件为r≤1/2,截断误差可达到O(τ2+h4+hτ22).当τ=O(h)时,此格式可逼近精度,特别当τ=O(h2)时,格式达到二阶精度.数值例子表明,所建立的差分格式是有效的.

This paper gives a three-layer explicit difference scheme with the dissipative term. Its local truncation error is in the order of O（x^2＋h^4＋τ^2/h^2）. Numerical examples shown that it is effective and practice consistent with theoretical analysis.