An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation. (English) Zbl 0990.65101

The authors present a new unconditionally stable implicit alterning direction implicit scheme of second order for the difference solution of a linear hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The resulting system is solved by a split method. A complete stability analysis is presented. Two numerical results are provided to demonstrate the efficiency and accuracy of the method.


65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
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