Stability analysis of alternate implicit schemes for 2-D second-order hyperbolic equations

Tian tian Zhang; Chang biao Yu; Ming yang Du; Wen wen Xu

doi:10.1117/12.2672453

28 March 2023 Stability analysis of alternate implicit schemes for 2-D second-order hyperbolic equations

Tian tian Zhang, Chang biao Yu, Ming yang Du, Wen wen Xu

Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 125970W (2023) https://doi.org/10.1117/12.2672453
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China

Abstract

In this paper, we study the Alternating Direction Implicit (ADI) format and stability of the linear 2-D second-order hyperbolic equation. The alternating direction implicit format with second-order accuracy is chosen in the time direction, and the initial conditions of the equation are discretized using second-order central difference, and the stability terms of the ADI format are obtained analytically using the separation of variables method. When the constant C and weighting coefficients r satisfy certain conditions, the alternating direction implicit form of the two-dimensional second-order hyperbolic equation is stable for an arbitrary grid ratio. Finally, numerical experiments are conducted to obtain numerical and exact solutions and their images of the equations to verify the correctness of the theoretical analysis.

Citation Download Citation

Tian tian Zhang, Chang biao Yu, Ming yang Du, and Wen wen Xu "Stability analysis of alternate implicit schemes for 2-D second-order hyperbolic equations", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 125970W (28 March 2023); https://doi.org/10.1117/12.2672453

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