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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.

MSC:

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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References:

[1] Mohanty, J Comp Appl Math 70 pp 231– (1996) · Zbl 0856.65098
[2] Lees, J Soc Indust Appl Math 10 pp 610– (1962) · Zbl 0111.29204
[3] Twizell, BIT 19 pp 378– (1979) · Zbl 0441.65066
[4] Jain, Int J Num Meth Eng 10 pp 960– (1976) · Zbl 0333.65047
[5] Iyengar, Int J Num Meth Eng 12 pp 1623– (1978) · Zbl 0383.65056
[6] Numerical solution of differential equations, 2nd Ed., New York: Wiley Eastern Ltd, 1984.
[7] Mckee, J Inst Math Applics 11 pp 105– (1973) · Zbl 0259.65085
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