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 steps
is expanded in powers of . We prove that the well-known expansion
for ordinary differential equations (an expansion in negative powers
of ) is perturbed by additional terms with non-negative powers of
for semi–explicit differential–algebraic equations of index one.
Hence, extrapolation in
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.