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Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Author

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  • María Consuelo Casabán

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, Access C, 2nd Floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • Rafael Company

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, Access C, 2nd Floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • Lucas Jódar

    (Instituto Universitario de Matemática Multidisciplinar, Building 8G, Access C, 2nd Floor, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

Abstract

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

Suggested Citation

  • María Consuelo Casabán & Rafael Company & Lucas Jódar, 2021. "Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:206-:d:483585
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    Citations

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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.
    2. Casabán, M.-C. & Company, R. & Jódar, L., 2023. "Numerical difference solution of moving boundary random Stefan problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 878-901.
    3. Casabán, M.-C. & Company, R. & Egorova, V.N. & Jódar, L., 2024. "A random free-boundary diffusive logistic differential model: Numerical analysis, computing and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 55-78.

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