Numerical solution of ordinary differential equations: introduction to the computational modeling of thixotropic fluids

• Grant number: 20/05966-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2020
• End date: January 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Bruno Pinheiro Toniato
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

In this project, we will investigate the numerical solution of Ordinary Differential Equations (ODEs). In particular, we will focus a specific equation, which is used for modeling the mechanical behavior of thixotropic fluids. The thixotropic is a mechanical response of the material, which can be mathematically modelled by kinematic-type equations for a structural parameter of the fluid. Due to the difficulty of obtaining analytical solutions for these equations, in this project the classical finite difference methods for ODEs will be analyzed. In addition, we will apply machine-learning techniques for estimating the numerical solution. (AU)