Spectral method for the heat equation with axial symmetry and a source

Abstract EN

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 Galerkin type with a Gauss-Radau numerical quadrature formula, it is based on a weighted weak variational formulation of the 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.