Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions

Authors

Vinícius F. Wasques^{1, *,} , Estevão Esmi², Laécio C. Barros², Peter Sussner^2,

¹Department of Mathematics, São Paulo State University, Avenida 24-A, Rio Claro, 13506-900, Brazil

²Department of Applied Mathematics, University of Campinas, Sérgio Buarque de Holanda Rua Sérgio Buarque de Holanda, Campinas, 13083-859, Brazil

^*Corresponding author. Email: vwasques@outlook.com

DOI

10.2991/ijcis.d.200916.001How to use a DOI?

Keywords

Fuzzy initial value problem; Sup-J extension principle; Interactive fuzzy numbers; Chemical reactions

Abstract

This paper studies numerical solutions for fuzzy initial value problems, where the initial conditions are given by interactive fuzzy numbers. The fuzzy solution is given by a numerical method that employs the arithmetic of interactive fuzzy numbers and yields a fuzzy number at each instant of time. The computational cost of the numerical method is also provided. The chemical decay reaction model is considered in order to illustrate that different types of interactivity produce different solutions for initial value problems. In addition, we present an application to the Lotka–Volterra model of oscillating chemical reactions.

Copyright

© 2020 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Vinícius F. Wasques
AU  - Estevão Esmi
AU  - Laécio C. Barros
AU  - Peter Sussner
PY  - 2020
DA  - 2020/09/24
TI  - Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions
JO  - International Journal of Computational Intelligence Systems
SP  - 1517
EP  - 1529
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200916.001
DO  - 10.2991/ijcis.d.200916.001
ID  - Wasques2020
ER  -