Conditional full stability of positivity-preserving finite difference scheme for diffusion-advection-reaction models
| Autor: | LUCAS JODAR, Vera Egorova, Rafael Company Rossi |
|---|---|
| Přispěvatelé: | Universidad de Cantabria |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Finite difference
Work (thermodynamics) Advection Applied Mathematics Numerical analysis Semi-discretization 010103 numerical & computational mathematics 01 natural sciences Stability (probability) 010101 applied mathematics Computational Mathematics Diffusion advection-reaction Reaction model Finite difference scheme Applied mathematics 0101 mathematics Diffusion (business) MATEMATICA APLICADA Diffusion–advection-reaction Exponential time differencing Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics, 2018, 341, 157-168 UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| Popis: | [EN] The matter of the stability for multidimensional diffusion-advection-reaction problems treated with the semi-discretization method is remaining challenge because when all the stepsizes tend simultaneously to zero the involved size of the problem grows without bounds. Solution of such problems is constructed by starting with a semi-discretization approach followed by a full discretization using exponential time differencing and matrix quadrature rules. Analysis of the time variation of the numerical solution with respect to previous time level together with the use of logarithmic norm of matrices is the basis of the stability result. Sufficient stability conditions on stepsizes, that also guarantee positivity and boundedness of the solution, are found. Numerical examples in different fields prove its competitiveness with other relevant methods. (C) 2018 Elsevier B.V. All rights reserved. This work has been partially supported by the Ministerio de Economia y Competitividad Spanish grant MTM2017-89664-P. |
| Databáze: | OpenAIRE |
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