Document Type

Poster

Abstract

This project extends previous work on free parameter methods for first-order differential equations (DE’s) by investigating the stability of explicit free parameter multistep methods for second-order DE’s. A method is stable if roundoff error in subsequent approximations does not grow exponentially. Dahlquist’s First Stability Barrier caps the maximum order of a stable method: by choosing to not maximize the order, we can add free parameters to a general multistep method, using these to optimize other properties; for example, varying these free parameters changes the size and shape of a method’s stability domain. We benchmark our results against the standard Stormer "methods."

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Publication Date

4-2022

Keywords

first-order differential equations, second-order differential equations, Dahlquist's First Stability Barrier

Disciplines

Mathematics

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