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Multiple shooting for unstructured nonlinear differential-algebraic equations of arbitrary index. (English) Zbl 1086.65086

The authors use multiple shooting techniques in the numerical solution of nonlinear boundary value problems for systems of differential algebraic equations (DAEs) of arbitrary index. Results concerning the solution and formulation of systems of general nonlinear DAEs are presented and a theorem on the local uniqueness of solutions of boundary value problems for DAEs is stated and proved.
The authors present an implementable multiple shooting technique, using a Gauss-Newton-like method, and establish the superlinear convergence of the method. Nonlinear projections are used to obtain consistent initial values and alternative ways of overcoming the problem of dealing with inconsistent intermediate iterates are suggested.
Results of applying the new method are illustrated by numerical examples which include the modelling of a pendulum in two space dimensions and the Lotka-Volterra system for a predator/prey interaction. The examples presented demonstrate the ability of the new method to solve problems with different values of the index and different structures, and also its good convergence properties.
Reviewer: Pat Lumb (Chester)

MSC:

65L80 Numerical methods for differential-algebraic equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

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