Mixed spectral method for heat transfer with inhomogeneous Neumann boundary condition in an infinite strip

In this paper, we develop a direct spectral method based on the mixed Laguerre–Legendre quasi-orthogonal approximation for non-isotropic heat transfer with inhomogeneous Neumann boundary condition in an infinite strip. This method guarantees that the homogeneous boundary condition is exactly satisfied, which differs from other spectral methods for Neumann problems. For analyzing the numerical errors, some basic results on the mixed Laguerre–Legendre quasi-orthogonal approximation are established. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide well with the theoretical analysis.