{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-comparison-of-a-few-numerical-schemes-for","title":"A comparison of a few numerical schemes for the integration of stochastic differential equations in the Stratonovich interpretation","arxiv_id":"1102.4401","date":"2011-02-22","proceeding":null,"authors":["David Garcia-Alvarez"],"abstract":"Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and derivative-free Milstein. The strong (path-wise) convergence is studied for each method by comparing the final points after integrating with $2^n$ and $2^{n-1}$ time steps. We also compare the time that the computer takes to carry out the integration with each scheme. Putting both things together, we conclude that, at least for our system, the Heun method is by far the best performing one.","url_abs":"http://arxiv.org/abs/1102.4401v1","url_pdf":"http://arxiv.org/pdf/1102.4401v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-comparison-of-a-few-numerical-schemes-for","repo_url":"https://github.com/FIshikawa/ExpressiveMonteCarlo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}