Abstract

In this paper, we present a spectral method for solving the heat equation in cylindrical coordinates in a case where the data are axisymmetric and independent of the z-coordinate at the same time. The spectral method considered is of GalerkintypewithaGauss-Radaunumericalquadratureformula, itisbasedonaweightedweakvariationalformulationofthe continuous problem. The method considered is discret only in r-variable, the time variable remains continuous. Consequently, the discret problem leads to a system of ordinary differential equations, we solve the system and estimate the error, we also give some numerical examples.