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

Casabán, María Consuelo; Company, Rafael; Jódar, Lucas

doi:10.3390/math9030206

Open AccessArticle

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

by

María Consuelo Casabán

^†

,

Rafael Company

^*,†

and

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

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2021, 9(3), 206; https://doi.org/10.3390/math9030206

Submission received: 21 December 2020 / Revised: 16 January 2021 / Accepted: 18 January 2021 / Published: 20 January 2021

(This article belongs to the Special Issue Mathematical Methods, Modelling and Applications)

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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.

Keywords: random mean square parabolic model; finite degree of randomness; monte carlo method; random finite difference scheme

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MDPI and ACS Style

Casabán, M.C.; Company, R.; Jódar, L. Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness. Mathematics 2021, 9, 206. https://doi.org/10.3390/math9030206

AMA Style

Casabán MC, Company R, Jódar L. Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness. Mathematics. 2021; 9(3):206. https://doi.org/10.3390/math9030206

Chicago/Turabian Style

Casabán, María Consuelo, Rafael Company, and Lucas Jódar. 2021. "Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness" Mathematics 9, no. 3: 206. https://doi.org/10.3390/math9030206

APA Style

Casabán, M. C., Company, R., & Jódar, L. (2021). Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness. Mathematics, 9(3), 206. https://doi.org/10.3390/math9030206

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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