Title | GALERKIN SPECTRAL METHOD FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS ARISING IN THERMAL CONVECTION |
Publication Type | Journal Article |
Year of Publication | 2002 |
Authors | Papanicolaou N., Christov C. |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 94 |
Pagination | 71-83 |
ISSN | 0205-0808 |
Keywords | beam functions, natural convection, spectral methods |
Abstract | In the present work we develop a Galerkin spectral technique for solving coupled higher-order boundary value problems arising in continuum mechanics. The set of so-called beam functions are used as a basis together with the harmonic functions. As featuring examples we solve two fourth-order boundary value problems related to the convective flow of viscous liquid in a vertical slot and a coupled convective problem. We show that the rate of convergence of the series is fifth-order algebraic both for linear and nonlinear problems of fourth order. The coupled problem exhibits fourth- and fifth-order convergence for the different unknown functions. Though algebraic, the fourth order rate of convergence is fully adequate for the generic problems under consideration, which makes the new technique a useful tool in numerical approaches to convective problems. |
2000 MSC | 37L65, 74S25, 76M22, 76E06, 76R10 |
Attachment | Size |
---|---|
94-071-083.pdf | 1.09 MB |