document: A collocation formulation of multistep methods for variable step-size extensions Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid . To make them practically useful , they have to be implemented by varying the step-size according to some error-control algorithm . It is well known how to extend Adams and BDF formulas to a variable step-size formulation . In this paper we present a collocation approach to construct variable step-size formulas . We make use of piecewise polynomials to show that every k-step method of order k +1 has a variable step-size polynomial collocation formulation
doc_bio_tags: O B I O B I O O O O B I O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I
extractive_keyphrases: multistep methods collocation formulation difference operators equidistant time grid piecewise polynomials
abstractive_keyphrases: variable step-size extensions error-control algorithm k-step method variable step-size polynomial collocation formulation