An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions

摘要

A new three level implicit unconditionally stable operator splitting method of O(k2+h2) is proposed for the numerical solution of two space dimensional linear hyperbolic equation utt+2α(x,y,t)ut+β2(x,y,t)u=A(x,y,t)uxx+B(x,y,t)uyy+f(x,y,t), 00 subject to appropriate initial and Dirichlet boundary conditions, where α(x,y,t)>β(x,y,t)>0, A(x,y,t)>0, B(x,y,t)>0. The resulting system of algebraic equations is solved by two-step split method. The proposed method is applicable to the problems having singularity at x=0. Numerical results are provided to demonstrate the utility of the new method.