 A multigrid preconditioned numerical scheme for a reaction–diffusion systemSamir Kumar Bhowmik Applied Mathematics and Computation, 2015, vol. 254, issue C, 266-276 Abstract: Reaction diffusion operators have been used to model many engineering and biological systems. In this study we consider a reaction diffusion system modeling various engineering and life science problems. There are many algorithms to approximate such mathematical models. Most of the algorithms are conditionally stable and convergent. For a big time step size a Krylov subspace type solver for such models converges slowly or oscillates because of the presence of the diffusion term. Here we study a multigrid preconditioned generalized minimal residual method (GMRES) for such a model. We start with a five point scheme for the spatial integration and a method of lines for the temporal integration of the system of PDEs. Then we implement a multigrid iterative algorithm for the full discrete model, and show some numerical results to demonstrate the dominance of the solver. We analyze the convergence rate of such a multigrid iterative preconditioning algorithm. Reaction diffusion systems arise in many mathematical models and thus this study has many applicabilities. Keywords: Reaction–diffusion system; Gray Scot model; Predator prey model; Finite difference scheme; Multigrid solver (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:254:y:2015:i:c:p:266-276 DOI: 10.1016/j.amc.2014.12.062 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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