Title

On a Numerical Method for Solution of the Mathieu-Hill Type Equations

Abstract

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.

Department(s)

Mechanical and Aerospace Engineering

Keywords and Phrases

Numerical Analysis; Equations

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1980 American Society of Mechanical Engineers (ASME), All rights reserved.

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