GALERKIN SPECTRAL METHOD FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS ARISING IN THERMAL CONVECTION

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.