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.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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