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Rosenbrock methods for differential algebraic equations. (English) Zbl 0613.65076
This paper deals with the numerical solution of differential algebraic equations (DAE) of index one. It begins with the development of a general theory on the Taylor expansion for the exact solutions of these problems, which extends the well known theory of Butcher for first order ordinary differential equations to DAE’s of index one. As an application, we obtain Butcher-type results for Rosenbrock methods applied to DAE’s of index one and we characterize numerical methods as applications of certain sets of trees. We derive convergent embedded methods of order 4(3) which require 4 or 5 evaluations of the functions, 1 evaluation of the Jacobian and 1 LU factorization per step.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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