Differential Equations and Numerical Analysis Seminar - 27/11/2013

Wednesday, 27 November 2013, 2:00 p.m.

Lecturer: Magda Rebelo  (CMAT/IST; FCT-UNL)

Title: "An overview of my recent work: numerical methods for differential equations of fractional order and a meshfree method for Brinkmann systems".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: In this seminar I will present an overview of recent work developed by me and my collaborators.

On the first part of the seminar I will present numerical methods for initial and boundary value problems for fractional di erential equations. The approach used is based on the equivalence between this kind of problems and Volterra integral equations (for initial value problems) or Fredholm integral equations (for boundary value problems). In general the solution of these equations are not smooth near the left endpoint of the interval of integration. Taking into account this behavior of the solution of such problems at the origin, we propose a collocation method based on a piecewise non-polynomial approximation of the solution. In order to illustrate the performance of the proposed method, several numerical examples are presented. This is a joint work with Luisa Morgado from Universidade de Trás-os-Montes e Alto Douro and Neville Ford from Chester University, Chester, UK.

On the second part of the seminar I will present a meshfree method for the numerical solution of Brinkman systems with Dirichlet and Neumann boundary conditions. This is a joint work with Nuno Martins from Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa. In this work we propose a representation for the  fluid  flow as a linear superposition of unsteady Stokeslets and elastodynamic P and S waves. Several numerical examples are presented in order to illustrate and discuss the feasibility of the method.