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Analysis and implementation of exponential finite difference method for stationary problems

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


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.

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