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An exponential spectral deferred correction method for multidimensional parabolic problems

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  • Wang, Yurun
  • Liu, Fei

Abstract

We present some efficient algorithms based on an exponential time differencing spectral deferred correction (ETDSDC) method for multidimensional second and fourth-order parabolic problems with non-periodic boundary conditions including Dirichlet, Neumann, Robin boundary conditions. Similar to the Fourier spectral method for periodic problems, the key to the efficiency of our algorithms is to construct diagonal discrete linear operators via Legendre–Galerkin methods with Fourier-like basis functions. In combination with the ETDSDC scheme, the proposed methods are spectrally accurate in space and up to 10th-order accurate in time (as shown in this work). We demonstrate the high-order of convergence and efficiency of our algorithms in solving parabolic equations through a series of two-dimensional and three-dimensional examples including Ginzburg–Landau and Allen–Cahn equations.

Suggested Citation

  • Wang, Yurun & Liu, Fei, 2025. "An exponential spectral deferred correction method for multidimensional parabolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 245-262.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:245-262
    DOI: 10.1016/j.matcom.2024.09.003
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    References listed on IDEAS

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    1. Yongho Kim & Gilnam Ryu & Yongho Choi, 2021. "Fast and Accurate Numerical Solution of Allen–Cahn Equation," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, December.
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