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Numerical treatment of retarded differential-algebraic equations by collocation methods. (English) Zbl 0891.65080

The author presents an algorithm for tracking jump discontinuities occurring in the numerical solution by collocation methods of retarded differential-algebraic equations of up to index 2 with state dependent delay. The algorithm is shown to preserve the order of the underlying collocation method and some numerical examples are given to suppport this.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34K05 General theory of functional-differential equations
34A34 Nonlinear ordinary differential equations and systems
34A09 Implicit ordinary differential equations, differential-algebraic equations
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