Volume 1, pp. 1-10, 1993.

Analysis of the linearly implicit mid-point rule for differential-algebraic equations

Claus Schneider

Abstract

The error of the linearly implicit mid–point rule after 2m+1 steps is expanded in powers of m2. We prove that the well-known expansion for ordinary differential equations (an expansion in negative powers of m2) is perturbed by additional terms with non-negative powers of m2 for semi–explicit differential–algebraic equations of index one. Hence, extrapolation in m2 will be of limited value only. The complete expansion shows these limits and, furthermore, can be used to derive an order 8 method of Rosenbrock type.

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Key words

Differential–algebraic equations, linearly implicit mid–point rule, Rosenbrock–type methods, extrapolation.

AMS subject classifications

65L05, 65B05, 58F99.