A meshless method for the numerical computation of the solution of steady Burgers-type equations

Authors:
A. Bouhamidi;M. Hached;K. Jbilou
Affiliations:
Université du Littoral Côte dOpale, LMPA, 50 rue F. Buisson, BP699, F-62228 Calais Cedex, France;IUT A, Université des Sciences et Technologies de Lille, Laboratoire Painlevé UMR 8524, Le Recueil - Rue de la Recherche - BP 90179, 59653 Villeneuve dAscq Cedex, France;Université du Littoral Côte dOpale, LMPA, 50 rue F. Buisson, BP699, F-62228 Calais Cedex, France
Venue:
Applied Numerical Mathematics
Year:
2013

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Abstract

In this paper, we discuss a meshless method for solving steady Burgers-type equations with Dirichlet boundary conditions. The numerical approximation of the solution in the given domain is obtained by using thin plate spline approximation, leading to a large-scale nonlinear matrix equation. The main difficulty of the proposed method is the numerical computation of a solution of the derived nonlinear matrix equation. We will show how to combine Newton@?s method with some matrix Krylov subspace techniques such as the global GMRES to solve these nonlinear problems. Numerical examples are given to illustrate the proposed method.