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Overview of Adaptive Shooting Methods for Boundary Value Problems

Josef Otta
Organization: Západočeská univerzita v Plzni

2005 Wolfram Technology Conference
Conference location

Champaign IL

The topic of this work is a proposal of adaptive numerical methods for the nonlinear boundary value problem for ordinary differential equations. The first part of my speech includes the 1D adaptive shooting method, where approximation of Fučík’s spectrum of

u''(t)+λ+ max(u(t),0) - λ- max(-u(t),0) = 0, u(0)=0, u(π)=0

is presented as an application of our designed method.

The 2D shooting method based on geometrical adaptive methods and statistical approach is presented in the second part. This method can be used for solving nonlinear boundary value problems with periodic conditions. As an application of this method a numerical approximation of ordinary differential equations with jumping nonlinearities describing a 1D model of a suspension bridge is presented.

*Engineering > Mechanical and Structural Engineering
*Mathematics > Calculus and Analysis > Differential Equations
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