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A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation

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  • Luo, Zhendong
  • Teng, Fei

Abstract

In this study, we devote ourselves to the reduced-order extrapolated finite difference iterative (ROEFDI) modeling and analysis for the two-dimensional (2D) Sobolev equation. To this end, we first establish the reduced-order extrapolated finite difference iterative (ROEFDI) scheme holding sufficiently high accuracy but containing very few degrees of freedom for the 2D Sobolev equation via the proper orthogonal decomposition (POD) technique. And then, we analyze the stability and convergence of the ROEFDI solutions. Finally, we use the numerical experiments to verify the feasibility and effectiveness of the ROEFDI scheme.

Suggested Citation

  • Luo, Zhendong & Teng, Fei, 2018. "A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 374-383.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:374-383
    DOI: 10.1016/j.amc.2018.02.022
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    References listed on IDEAS

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    1. Luo, Zhendong & Jin, Shiju & Chen, Jing, 2016. "A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 396-408.
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    Cited by:

    1. Nikan, O. & Avazzadeh, Z., 2021. "A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    2. Zeng, Yihui & Luo, Zhendong, 2022. "The Crank–Nicolson mixed finite element method for the improved system of time-domain Maxwell’s equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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