Mixed Pseudospectral Method for Heat Transfer

Abstract

In this paper, we propose a mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer with inhomogeneous boundary conditions on an infinite strip. Some properties about the mixed generalized Laguerre-Legendre approximation are established. By reformulating the equation with suitable functional transform defined on an infinite strip, a mixed Laguerre-Legendre pseu-dospectral scheme is constructed. Its convergence is proved. Numerical results are presented to demonstrate the efficiency of this new approach and to validate our theoretical analysis.

Keywords:

• mixed Laguerre-Legendre approximation
• pseudospectral method for heat transfer
• inhomogeneous Dirichlet boundary condition
• infinite strip

AMS Subject Classification:

• 65M70
• 35K05
• 35K99
• 35R15
• 41A30