In this paper, we consider the non-isotropic heat transfer in an infinite strip. A straightforward approach is to truncate the infinite strip into a sufficiently large subdomain and impose certain artificial boundary conditions.

The aim of this paper is to develop the mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer in an infinite strip, by using the Legendre interpolation in the direction of finite length, and the generalized Laguerre function interpolation in the infinite long direction.

In order to analyze the numerical errors of non-isotropic heat transfer in an infinite strip, we need the next following orthogonal projection.

In this paper, we studied numerical simulation of non-isotropic heat transfer with Dirichlet boundary condition in an infinite strip. Since its solution decays exponentially as x [right arrow] [infinity], it is better to use the Laguerre functions [e.sup.-1/2 [beta]x] [L.sup.([beta]).sub.l] (x) as the basis functions.

Moreover, we could combine the idea of [22] and this paper to design and analyze spectral methods for various mixed inhomogeneous boundary value problems defined on infinite strip. We shall report the related results in the future.

Mixed spectral method for Navier-Stokes equations in an infinite strip by using generalized Laguerre functions.

Mixed spectral method for heat transfer with inhomogeneous Neumann boundary condition in an infinite strip. Applied Numerical Mathematics, 92:82-97, 2015.

Mixed generalized Laguerre-Legendre spectral method for heat transfer in an infinite strip. In Computational Sciences and Optimization (CSO), 2012 Fifth International Joint Conference on, pp.

Westpfahl, "Diffraction of plane waves by an infinite strip grating," Ann.

[20.] Liineburg, E., "Diffraction by an infinite set of parallel half-planes and by an infinite strip grating," Analytical and Numerical Methods in Electromagnetic Wave Theory, M.

Material is presented in logical order, rather than chronological order of discovery, from the heat operator and mean values through subtemperatures and the Dirichlet problem, temperature on an

infinite strip, green functions and heat potentials, polar sets and thermal capacity, and thermal fine topology.