Numerical methods for partial differential equations and their applications in solving problems

Abstract

The student has already been developing the present project inscribed on the Program of Scientific Initiation of UNESP - without scholarship ICSB/PROPe 2017/2018 - Rule 15/2016 - PROPe, duration from 01/04/2017 a 31/03/2018. The analysis of this proposal by FAPESP may offer to the student an opportunity to study a full time for the development of this project, because he may will have a scholarship for that, in case it will be approved. In this project, the student will study and implement numerical methods for partial differential equations (PDE) by using the finite difference technique. The concepts about convergence, stability and consistence will be studied theoretically by typical equations and verified in practical by implementing examples in some computational language, such as, Matlab, Scilab, Maple or Octave. It is supposed to apply the numerical techniques studied for solving physical problems, which are modeled, by those kind of equations, taking mainly account problems, as toy models, from computational fluid dynamics adapted for the level of student education. (AU)