解四阶抛物型方程的高精度显式差分格式

Explicit Difference Scheme of High Accuracy for Solving Four-Order Parabolic Equation

对四阶抛物型方程ut+uxxxx=0,构造一个新的三层显式差分格式,其稳定性条件和局部截断误差阶分别为r=τ/h4≤1/8和O(2τ+h6),其结果优于其他四阶抛物型方程的结果.数值例子表明,理论分析是正确的,该格式是有效的.

In this paper,a three-level explicit difference scheme is proposed for solving four-order parabolic equation ut＋uxxxx=0.The scheme meets a stability condition of r=τ/h4≤1/8 and shows a local truncation error of O（τ2＋h6）.It is showed that the scheme is effective and the analysis of stability is right by a numerical example.