2023 , Volume 28, № 2, p.4-18

In spectral models of dynamo systems, solutions are represented as linear combinations of a finite number of stationary basis fields (modes). The modes themselves are the solution to some spectral problems. From the physical point of view the most natural are the modes consisting of oscillations, which could be free or damping.

To developed a model, it is necessary to determine the modes parameters and eigenvalues and then calculate the Galerkin coefficients. The purpose of the paper is to develop a computing technology for automating these calculations.

The technology is based on computer algebra methods. The Galerkin coefficients are integrals of very complex expressions. Therefore, correct determination of the integrand is a difficult problem. Here, it is convenient to use computer algebra systems (CAS). Coefficients are measures of mode interaction so whether the coefficient is exactly zero or not, seem to be important. The identification of zero coefficients using CAS can be done analytically.

The paper thoroughly describes a technology for automated calculation of the basis modes and Galerkin coefficients using the Maple package. The case of an axisymmetric kinematic dynamo is considered. A description of the calculations for the complete system of magnetohydrodynamic convection would be very long. However, the general idea is clear for the described case.

The proposed technology allows quick and accurate generating of various spectral models by varying the mode sets.

It seems to be useful for the study of dynamos using spectral models.