关于色散方程的一类三阶显格式

A Kind of Explict Difference Scheme Having Three Order for Dispersion Equation

构造了一类求解色散方程Ut=auxx的双参数显格式 ,其截断误差阶是O(τ +h3)并分析了格式的稳定性 .指出当参数是网比r的适当函数时 ,格式的稳定性条件为 |r| 1 /4.本文分析方法巧妙 .它是目前集精确度 ,稳定性条件最好的三层显格式 .数值例子验证了分析的结果 .而且从数值例子中可以看出 ,随时间层的增多 。

A Kind of explicit difference schemes with two parameters for the dispersion equation u t=au xxx are proposed by this paper here. The truncation errors of the schemes ate first order in time and three order in space.We analyze the stability of schemes and point out when we propriety choose the parameters,the condition of stable is r｜1/4. We give a good way to analyze the question.For the present,they are the perfect three level explicit difference schemes which have good accuracy,stability.The numerical examples have proved the result of theoretical analysis.From the stable,we find when increase the level of the time,the error increase slowly.