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A new simultaneously compact finite difference scheme for high-dimensional time-dependent PDEs

Author

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  • Doostaki, Reza
  • Hosseini, Mohammad Mehdi
  • Salemi, Abbas

Abstract

This paper presents a new compact finite difference scheme for solving linear high-dimensional time-dependent partial differential equations (PDEs). Despite the different spatial and time conditions in time-dependent problems, we propose a new compact finite difference scheme simultaneously both in time and space with arbitrary order accuracy. The merit of the proposed method is that the approximation of partial derivatives are derived simultaneously at all grid points. Also, by substituting the partial derivatives in the linear time-dependent PDEs a linear system of equations is derived. To show the efficiency and applicability of the proposed method, the fourth, sixth, and eighth-order simultaneously compact finite difference schemes are used for solving parabolic and convection–diffusion equations which have both time and spatial partial derivatives. The numerical results show the accuracy of the proposed method.

Suggested Citation

  • Doostaki, Reza & Hosseini, Mohammad Mehdi & Salemi, Abbas, 2023. "A new simultaneously compact finite difference scheme for high-dimensional time-dependent PDEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 504-523.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:504-523
    DOI: 10.1016/j.matcom.2023.05.008
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    References listed on IDEAS

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    1. Sun, Jie & Eichholz, Joseph A., 2018. "Splitting methods for differential approximations of the radiative transfer equation," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 140-150.
    2. Dehghan, Mehdi & Mohebbi, Akbar, 2008. "High-order compact boundary value method for the solution of unsteady convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 683-699.
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