Numerical solution for Interval Initial Value Problems based on interactive arithmetic
Publish place: 9th Iranian Joint Congress on Fuzzy and Intelligent Systems
Publish Year: 1400
نوع سند: مقاله کنفرانسی
زبان: English
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شناسه ملی سند علمی:
FJCFIS09_071
تاریخ نمایه سازی: 10 اردیبهشت 1401
Abstract:
This work presents a study of Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative (gH-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the gH-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation presented in the method is adapted for intervals. The arithmetic considered here is obtained from the sup-J extension principle, where J is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via gH-derivative. To illustrate the results, the paper focuses in the decay Malthusian model.
Keywords:
Interval initial value problem , Generalized Hukuhara derivative , Euler method , Malthusian model , Interactivity
Authors
Estev˜ao Esmi,
dept. Applied Mathematics, University of Campinas, Campinas, Brazil
Cristina Sacilotto,
dept. Applied Mathematics, University of Campinas, Campinas, Brazil
Vin´ıcius F. Wasques
dept. Mathematics, S˜ao Paulo State University, Rio Claro, Brazil,Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Brazil
La´ecio C. Barros
dept. Applied Mathematics, University of Campinas, Campinas, Brazil