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New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations. (English) Zbl 1181.65112

Summary: New unconditionally stable implicit difference schemes for the numerical solution of multi-dimensional telegraphic equations subject to appropriate initial and Dirichlet boundary conditions are discussed. Alternating direction implicit methods are used to solve two and three space dimensional problems. The resulting system of algebraic equations is solved using a tri-diagonal solver. Numerical results are presented to demonstrate the utility of the proposed methods.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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