To see how Mathieu functions arise in problems with elliptical boundary conditions, we need to formulate the relevant PDEs in elliptical coordinates.

In this section we investigate the effect that damping has on the transition curves of Mathieu’s equation by applying the two variable expansion method to the following equation, known as …

The behavior of the Mathieu functions is illustrated by using a variety of plot types with representative examples taken from mechanics. We show how Mathieu functions can be …

Mathieu's Equation Remark: Before proceeding, we recommend that you familiarize yourself with the basics of XPP syntax via the introductory examples ch1-riccati.ode and ch1-van-der …

The Mathieu and modified Mathieu functions are solutions to the ordinary differ-ential equations arising in the separation of the Helmholtz equation in two dimen-sions using elliptic …

This paper surveys and recapitulates the historical development of the theory and methods of computation for Mathieu functions and modi ed Mathieu functions and identi es some gaps in …

The condition for stability for the linearized equation, the Mathieu equation (as well as for a broader class of equations, Hill's Equation,) is then derived, also using Floquet Theory. Also …