拟谱-微分求积混合方法求解一类双曲电报方程

摘要

拟谱方法和微分求积法是两类重要的无网格法,二者都已在科学和工程计算中获得了广泛应用.采用拉格朗日插值多项式作为二者的试函数,且采用同一种网格点分布,指出了在空间域上,微分求积法是拟谱方法的一种特殊形式.在此基础上,结合二者各自的特点,提出了拟谱-微分求积混合方法用于求解一类双曲电报方程.理论分析和数值测试表明,新方法在空间域上具有谱精度收敛性,在时间域上是A-稳定的,比较适合于求解多维电报方程.%Pseudo-spectral method and differential quadrature method are two kinds of important meshfree methods,both of which have been widely used in scientific and engineering calculations.The Lagrange interpolation polynomials are used as the trial functions of the two methods,and the same distribution of grid points is used.This paper reveals that the differential quadrature method is a special form of the pseudo-spectral method.On this basis,a pseudo-spectral-differential quadrature coupled method (PSDQM) is proposed to solve a class of hyperbolic telegraph equations.Theoretical analysis and numerical tests show that the new method has spectral precision convergence in spatial domain and is Astable in time domain.And it is suitable for solving multi-dimensional telegraph equations.