A Study of Coupled Mathieu Equations by Use of Infinite Determinants

Hill’s method of infinite determinant is applied to solving a system of Mathieu-type equations. Expansion of the converging infinite determinant then leads to the criterion for stability of the solution. Numerical results are then presented in graphs for two examples. Good agreements between the present results and the existing solutions are observed. The criterion therefore is useful to predict the stability properties of a finite number of coupled Mathieu equations.