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An unconditionally stable spatial sixth-order CCD-ADI method for the two-dimensional linear telegraph equation

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Abstract

The telegraph equation is one of the important models in many physics and engineering. In this work, we discuss the high-order compact finite difference method for solving the two-dimensional second-order linear hyperbolic equation. By using a combined compact finite difference method for the spatial discretization, a high-order alternating direction implicit method (ADI) is proposed. The method is O(τ 2 + h 6) accurate, where τ, h are the temporal step size and spatial size, respectively. Von Neumann linear stability analysis shows that the method is unconditionally stable. Finally, numerical examples are used to illustrate the high accuracy of the new difference scheme.

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  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Dongdong He

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  1. Dongdong He
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He, D. An unconditionally stable spatial sixth-order CCD-ADI method for the two-dimensional linear telegraph equation. Numer Algor 72, 1103–1117 (2016). https://doi.org/10.1007/s11075-015-0082-7

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