Spectral Method for a Particular Case of the Heat Convection-Diffusion Equation

The purpose of this paper is to study the Legendre spectral method for solving a particular case of the heat convection-diffusion equation, wich is formulated as a mixed initial boundary value problem within the finite regular domain Λ = (−1, 1). To tackle this problem, we employ certain techniques to transform it into a system of ordinary differential equations. Through matrix analysis, we derive a general term that characterizes all the ordinary differential equations in this system. solving this general term, provides the desired approximate solution, and we also present the error estimation.