色散方程的四点显式差分格式

本文对色散方程u_t=au>_xxx构造了一类高稳定性的、在中间层涉及四个网格点的三层显式差分格式,其局部截断误差为O(τ+h),其稳定条件为|R|=|α|τ/h3≤0.25至|R|≤10,它们较大地改善了同类格式的稳定条件|R|≤0.251].

Four-Point Explicit Difference Schemes for the Dispersive Equation

A class of three-level explicit difference shcemes for the dispersive equation ut= au are established. These schemes have higher stability and involve four mesh points at the middle level. Their local, truncation errors are 0(r+h) and stability conditions are from |R|<0.25 to |R|<10, where R = ar/h3, which is much better than |R|<0.25.