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

Saburi Rasheed, Olaniyi S. Iyiola and Bruce A. Wade

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 538-557

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.

Keywords: Exponential integrators; Reaction–diffusion systems; Stiff systems; Turing patterns; Strang splitting (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:538-557

DOI: 10.1016/j.matcom.2025.07.028

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