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Space–time discretizing dispersion relation preserving schemes for inhomogeneous damped wave equations

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  • Jaglan, Jyoti
  • Singh, Ankit
  • Rajpoot, Manoj K.

Abstract

This paper presents space-time discretization schemes using a partially implicit time-integration method with a fourth-order compact finite difference scheme for numerical simulation of damped linear and nonlinear wave equations. Despite being implicit in nature, inversion of the coefficient matrix for the present method is not necessary, which makes the developed method very efficient in terms of computational cost and complexity. Numerical properties of the present method are calibrated using Fourier-spectral analysis. Convergence analysis of the fully-discretized systems is established. Discrete energy errors for the developed method are computed for wave propagation in the homogeneous medium. Theoretical convergence rate is also validated numerically by considering the relative errors in the discrete L2-norm. The accuracy of the developed method is validated through a series of numerical experiments. Computed solutions match well with the results discussed in the literature.

Suggested Citation

  • Jaglan, Jyoti & Singh, Ankit & Rajpoot, Manoj K., 2026. "Space–time discretizing dispersion relation preserving schemes for inhomogeneous damped wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 587-612.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:587-612
    DOI: 10.1016/j.matcom.2026.03.029
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    References listed on IDEAS

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    1. Liao, Wenyuan & Yong, Peng & Dastour, Hatef & Huang, Jianping, 2018. "Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 385-400.
    2. Zlotnik, Alexander & Čiegis, Raimondas, 2022. "On higher-order compact ADI schemes for the variable coefficient wave equation," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
    4. Saleh, Mahmoud & Kovács, Endre & Nagy, Ádám, 2023. "New stable, explicit, second order hopscotch methods for diffusion-type problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 301-325.
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