Author(s)

Jay H. Wolkowisky

Abstract

This paper presents a general shooting method for two-point boundary value problems for ordinary differential equations. The method is applied using MATHEMATICA to the problem of a buckled plate resting on an elastic foundation. This problem has multiple solutions corresponding to the vari- ous buckled states which bifurcate from the unbuckled state. An algebraic problem with a cubic nonlinearity, analogous to the equations for the buck- led plate, is used with MATHEMATICA to explain the bifurcations in the buckling problem. 1 The Shooting Method In order to explain this version of the shooting method applied to two-point boundary value problems for a system of ordinary differential equations that contain a parameter, we first look at a simple example. Consider the following boundary value problem for a second-order dif- ferential equat

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