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A new second-order accurate Strang splitting type exponential integrator for semilinear parabolic problems

Author

Listed:
  • Rasheed, Saburi
  • Iyiola, Olaniyi S.
  • Wade, Bruce A.

Abstract

A novel exponential integrator is developed to address two-dimensional semilinear parabolic problems with both smooth and non-smooth boundary and initial conditions. This integrator is characterized by its computational efficiency, L-stability, parallelizability, and second-order accuracy. This method employs a rational function (non-Padé type), specifically, the real distinct pole (RDP), to estimate the matrix exponentials involved in the integration scheme. This novel Strang-splitting-type exponential time differencing (ETD) scheme is utilized to address various reaction–diffusion equations (RDEs) under homogeneous Dirichlet, Neumann, and periodic boundary conditions. The experimental results validate and confirm that the proposed exponential integrator is of second-order convergence rate. The examples provided demonstrate the superior accuracy and efficiency of this technique compared with existing second-order methods.

Suggested Citation

  • Rasheed, Saburi & Iyiola, Olaniyi S. & Wade, Bruce A., 2026. "A new second-order accurate Strang splitting type exponential integrator for semilinear parabolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 538-557.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:538-557
    DOI: 10.1016/j.matcom.2025.07.028
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    References listed on IDEAS

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    1. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
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