On a Numerical Method for Solution of the Mathieu-Hill Type Equations
This paper presents a computer-programmable numerical method for the solution of a class of linear, second order differential equations with periodic coefficients of the Mathieu-Hill type. The method is applicable only when the initial conditions are prescribed and the solution is not requiried to be periodic. The solution is facilitated by representing the coefficient functions as a sum of step functions over corresponding sub-intervals of the fundamental interval. During each sub-interval, the solution form is assumed to be that of the differential equations with "constant" coefficients. Constraint equations are derived from imposing the conditions of "compatibility" of response at the end nodes of the intermediate sub-intervals. This set of simultaneous linear equations is expressed in matrix form. The matrix of coefficients may be represented as a triangular one. This form greatly simplifies the solution process for simultaneous equations. The method is illustrated by its application to some specific problems.
A. Midha and M. L. Badlani, "On a Numerical Method for Solution of the Mathieu-Hill Type Equations," Journal of Mechanical Design, American Society of Mechanical Engineers (ASME), Jan 1980.
The definitive version is available at http://dx.doi.org/10.1115/1.3254794
Mechanical and Aerospace Engineering
Keywords and Phrases
Numerical Analysis; Equations
Article - Journal
© 1980 American Society of Mechanical Engineers (ASME), All rights reserved.