Construction and benchmarking of adaptive parameterized linear multistep methods

Abstract: A recent publication introduced a new way to define all k-step linear multistep methods of order k and k+1, in a parametric form that builds in variable step-size. In this framework it is possible to continuously change method and step-size, making it possible to create better behaving adaptive numerical solvers. In this thesis general numerical solvers based on this framework have been implemented, utilizing variable step-size and variable order, based on control theory and digital filters. To test and analyze the solvers, libraries of test problems, methods and filters have been implemented. In the analysis, the solvers were also compared to commercial (Matlab) solvers. The conclusion of this investigation is that the solvers show potential to become competitive in the field.