Korteweg-de-Vries方程有限谱数值格式

Finite spectral numerical scheme for korteweg-de-Vries equation

以kdV方程为模型,利用有限谱方法构造数值计算格式,检验有限谱法计算含有色散项的非线性方程的精度,并对孤立波的演化及孤立波的碰撞进行了数值模拟,结果说明有限谱数值格式能较准确地模拟孤立波的行为.同时,把有限谱数值格式的计算结果同解析解进行对比,结果表明有限谱法具有较高的精度.

A finite spectral method was applied to KdV equation to test the accuracy of finite spectral numerical schemes applied in nonlinear equation including the dispersive tenn. The wave propagation were calculated by FS scheme and solitary wave collision were simulated numeriaclly. The results show that the appropriate FS scheme can simulate solitary wave accurately. Comparisons between FS scheme and analytical solution were presented, and the results prove that the appropriate FS scheme is efficient and accurate.