Scilab Toolbox for Calculating of Mathieu Functions

Abstract

In this paper, we describe the functionality of the software package Mathieu Functions Toolbox, which is an module for the Scilab-free opensource program for mathematical and other calculations. The developed package allows to calculate the angular (periodic) and radial (modified, nonperiodic) Mathieu functions, their characteristic values and the Fourier expansion coefficients for a given order of a function, parameter and argument. The program allows you to search for the roots of the radial Mathieu functions for the Dirichlet and Neumann boundary conditions and calculate the modes of the vibrating elliptical membrane. The paper describes the functions of the developed package and demonstration programs.