Analysis and implementation of exponential finite difference method for stationary problems

• Grant number: 16/08343-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2016
• End date: December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Analice Costacurta Brandi
• Grantee: Beatriz Liara Carreira
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

The Poisson equation is a well-known class of elliptical partial differential equations and it is usually used to describe the motion of a viscous incompressible fluid at low velocity. The elliptic equation solution using the finite difference method results in a linear equations system, typically large and sparse, which requires iterative methods to solve them. In this context, this research project aims to study, implement, and compare the finite differences and finite differences exponential methods applied to the two-dimensional Poisson equation for different boundary conditions. Furthermore, iterative methods of linear equations solution will also be investigated to solve the problem. The obtained results will be compared to numerical results and analytical solutions existing in the literature, in order to analyze the convergence, efficiency, and, especially, the computational time spent in the numerical simulations.