The new alternating direction implicit difference methods for the wave equations.

*(English)*Zbl 1166.65044Summary: A new second-order alternating direction implicit (ADI) scheme, based on the idea of the operator splitting, is presented for solving two-dimensional wave equations. The scheme is also extended to a high-order compact difference scheme. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical examples are presented and the results are very satisfactory.

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35L05 | Wave equation |

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

65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |

65F10 | Iterative numerical methods for linear systems |

##### Keywords:

wave equation; compact difference scheme; error analysis; alternating direction implicit (ADI) scheme; operator splitting; unconditional stability; numerical examples
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\textit{J. Qin}, J. Comput. Appl. Math. 230, No. 1, 213--223 (2009; Zbl 1166.65044)

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