Finite difference solution for diffusion problems: numerical analysis and computational aspects

• Grant number: 19/10137-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2019
• End date: July 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Gilmar Francisco de Oliveira Santos
• 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 it will be investigated theoretical and computational aspects for solving diffusion problems in one and two dimensions. The theoretical studies will be concentrated in the finite difference approximations of functions and derivatives, and in the consistency and stability analyses of the numerical schemes. The implementations will be done in Python which is a robust, efficient and well supported programming language. Moreover, Python is also considered as an appropriate language for developing new codes using machine-learning algorithms. Therefore, in order to introduce the student in the scientific computing area, it will investigated some diffusion problems modelled by differential equations.