SciML/OrdinaryDiffEq.jl

Multistep Integrators for Second Order DiffEqs

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#331 opened on Apr 19, 2018

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Description

Gauss-Jackson: https://drum.lib.umd.edu/bitstream/handle/1903/2202/2004-berry-healy-jas.pdf?sequence=7 https://www.researchgate.net/publication/333300756_Accuracy_and_Efficiency_Comparison_of_Six_Numerical_Integrators_for_Propagating_Perturbed_Orbits

Berry-Healy: https://pdfs.semanticscholar.org/2166/2dcd9b7ece9f4abbb2e52154ae7a840ed0d6.pdf or https://pdfs.semanticscholar.org/4701/d1c3c9b1101c3e23b4472d4895aa5d7f9a51.pdf

Stormer-Cowell: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.573.319&rep=rep1&type=pdf and https://www.sciencedirect.com/science/article/pii/S037704270400250X and https://www.sciencedirect.com/science/article/pii/0377042794001020

Hairer I has sections on the implicit and explicit Stromer methods as well.

Interesting related result: https://researchspace.auckland.ac.nz/bitstream/handle/2292/4980/449.pdf?sequence=1

Contributor guide

Tech stack
None
Domain
datamachine learning
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
5
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
over 1 week
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
needs investigation
Prerequisites
Numerical analysis of ODEsJulia programmingUnderstanding of multistep methodsScientific computing background
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
10
Research direction
First, study the referenced papers (Gauss Jackson, Berry Healy, Stormer Cowell) and Hairer I to understand the algorithms for second order multistep integrators. Then, examine the existing integration infrastructure in OrdinaryDiffEq.jl to see how new integrators are added. Implement the methods following the package's patterns, and validate against known test problems. The issue has no prior comments or PRs, so this is a clean slate.