A Coupled Pseudospectral-Differential Quadrature Method for a Class of Hyperbolic Telegraph Equations

摘要

Pseudospectral methods and differential quadrature methods are two kinds of important meshless methods, both of which have been widely used in scientific and engineering calculation. The Lagrange interpolation polynomials are used as the trial function of the two methods, and the same distribution of grid points is used. This paper points out that the differential quadrature method is a special form of the pseudospectral method. On the basis of the above, a coupled pseudospectral- differential quadrature 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 has A-stability in time domain. And it is suitable for solving multidimensional telegraph equations.