Strong stability preserving multiderivative time marching methods for stiff reaction–diffusion systems

Jyoti Jaglan, Ankit Singh, Vikas Maurya, Vivek S. Yadav and Manoj K. Rajpoot

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 267-282

Abstract: The present study introduces a new class of unconditionally strong stability preserving (SSP) multi-derivative Runge–Kutta methods for the numerical simulation of reaction–diffusion systems in the stiff regime. The unconditional SSP property of the methods makes them highly efficient for the simulation of reaction–diffusion systems without any restrictive time-step requirements. These methods have been tested for accuracy using L∞ error analysis, and comparisons with existing literature have shown that they perform better even for larger time-steps. In addition, the robustness and efficiency of the derived method are also validated by numerical simulations of the Brusselator, Gray–Scott, and Schnakenberg models.

Keywords: Strong stability preserving; Multiderivative Runge–Kutta method; Positivity preserving; Reaction–diffusion systems; Time discretization; Pattern formation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:267-282

DOI: 10.1016/j.matcom.2024.05.020

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