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An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions. (English) Zbl 1077.65093
A new three level implicit unconditionally stable operator splitting method of $O(k^2+h^2)$ is proposed for the numerical solution of the two space dimensional linear hyperbolic equation $$u_{tt}+2\alpha(x,y,t)u_t+\beta ^2(x,y,t)u=A(x,y,t)u_{xx}+B(x,y,t)u_{yy}+f(x,y,t),$$ $0<x$, $y<1$, $t>0$ subject to appropriate initial and Dirichlet boundary conditions, where $\alpha(x,y,t)>\beta(x,y,t)>0$, $A(x,y,t)>0$, $B(x,y,t)>0$. 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.

65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
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