Semi-implicit Euler method: Difference between revisions

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Revision as of 23:30, 14 October 2024 edit Chaosand (talk \| contribs) 37 edits Clarified that the method had been "discovered" many times earlier. ← Previous edit		Latest revision as of 09:06, 15 April 2025 edit undo Citation bot (talk \| contribs) Bots 5,861,485 edits Altered date. Added class. \| Use this bot. Report bugs. \| Suggested by Abductive \| Category:Numerical differential equations \| #UCB_Category 16/167
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Line 3: == Origin == The method~~, however,~~ has been discovered and forgotten many times, dating back to Newton's ''Principiae'',<ref name="hairer2003" /> as recalled by Richard Feynman in his ''Feynman Lectures'' (Vol. 1, Sec. 9.6)<ref name="feynman1963" /> In modern times, the method was rediscovered in a 1956 preprint by René De Vogelaere that, although never formally published, influenced subsequent work on higher-order symplectic methods.<ref name="skeel2003" />▼ The method was accidentally discovered by [[Newton North High School]] senior student Abby Aspel in 1980. In a lab assignment simulating orbits using Kepler's Law, which required computation in [[BASIC]]: she accidentally reversed two lines of code by calculating velocity before position. Her simulation converged more quickly and resulted in more accurate and feasible results than what was expected. Alan Cromer then proved why her algorithm was more stable than previous methods of computation.<ref>{{Cite journal \|last=Cromer \|first=Alan \|date=1981-05-01 \|title=Stable solutions using the Euler approximation \|url=https://doi.org/10.1119/1.12478 \|journal=American Journal of Physics \|volume=49 \|issue=5 \|pages=455–459 \|doi=10.1119/1.12478 \|issn=0002-9505}}</ref> ▲The method, however, has been discovered and forgotten many times, dating back to Newton's ''Principiae'',<ref name="hairer2003" /> as recalled by Richard Feynman in his ''Feynman Lectures'' (Vol. 1, Sec. 9.6)<ref name="feynman1963" /> In modern times, the method was rediscovered in a 1956 preprint by René De Vogelaere that, although never formally published, influenced subsequent work on higher-order symplectic methods.<ref name="skeel2003" /> == Setting == Line 102 ⟶ 98: \| last2 = Cieśliński \| first2 = Jan L. \| date = 2020 \| title = On the famous unpublished preprint "Methods of integration which preserve the contact transformation property of the Hamilton equations" by René De Vogelaere \| class = math.NA \| eprint = 2003.12268 }}</ref>