【摘要】 提出一族组合型超紧致差分格式(CSCD),对CSCD的数值特性作了分析,并同其他中心型差分格式进行比较。从定性角度,得出同阶中心差分格式中,CSCD格式的截断误差系数最小的结论。从定量角度,利用Fou-rier分析方法分析了CSCD格式的分辨率,并同其他中心型差分格式比较,得出CSCD格式有较高的分辨率的结论。把10阶CSCD格式应用于KdV-Burgers方程和浅水方程的数值模拟,给出两个应用算例。数值实验表明CSCD格式不仅有理论上的高精度,而且有良好的稳定性和收敛性。更多还原

【Abstract】 A combined super compact finite difference scheme(CSCD) is proposed.Numerical characteristics of CSCD is analysed and compared with other symmetric difference schemes.The truncation error of CSCD is derived and compared with some symmetric finite difference methods having the same order of accuracy,which shows that CSCD has the smallest coefficients in error terms.By using Fourier analysis on the capability of resolution,we conclude that CSCD gives higher resolution,with respect to other symmetric finite difference methods.Tenth-order CSCD is applied to numerical simulation of KdV-Burgers equation and shallow water equations.Two tests are given.Numerical experiment point out that CSCD has properties of not only higher accuracy but also good stability and convergence.更多还原