RWPM: a software package of shooting methods for nonlinear two-point boundary value problems

doi:10.1016/0168-9274(93)90134-D

Applied Numerical Mathematics

Volume 13, Issues 1–3, September 1993, Pages 103-108

https://doi.org/10.1016/0168-9274(93)90134-D Get rights and content

Abstract

The aim of this paper is to present the numerical software package RWPM which solves linear and nonlinear two-point boundary value problems in ordinary differential equations. The package is based on multiple shooting and stabilized march techniques. Numerical examples demonstrating the efficiency of the package are presented.

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To apply appropriate techniques, we first transform the model into a two-point boundary value problem (BVP, Section 3). The resulting BVP and the corresponding extended systems for computation of bifurcations (Section 4) are solved using the well-approved software package RWPM [26–28]. In the following, we give an overview of this implementation of the model.
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We study the solution field $M$ of a parameter dependent nonlinear two-point boundary value problem presented by Troger and Steindl [H. Troger, A. Steindl, Nonlinear Stability and Bifurcation Theory, Springer, Wien, New York, 1991]. This problem models the buckling of a thin-walled spherical shell under a uniform external static pressure. The boundary value problem is formulated as an abstract operator equation T(x,λ)=0 in appropriate Banach spaces. By exploiting the equivariance of T, we obtain detailed informations about the structure of $M$ . These theoretical results are used to compute efficiently interesting parts of $M$ with numerical standard techniques. Bifurcation diagrams, a stability diagram and pictures of deformed shells are presented.
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RWPM: a software package of shooting methods for nonlinear two-point boundary value problems

Abstract

Appl. Math. Lett.

J. Comput. Appl. Math.

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

A semi-implicit midpoint rule for stiff systems of ODE's

Numer. Math.

Multiple shooting techniques revisited

Efficient shooting algorithms for solving nonlinear TPBVPs with separated endconditions

Shooting algorithms for two-point BVPs

RWPM, a multiple shooting code for nonlinear two-point boundary value problems: version 4

Shooting methods for two-point BVPs with partially separated endconditions, Part I