刚性常微分方程的自适应时步法半隐式一步泰勒方案

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-18 DOI:arxiv-2409.11990

S. Boscarino, E. Macca

{"title":"刚性常微分方程的自适应时步法半隐式一步泰勒方案","authors":"S. Boscarino, E. Macca","doi":"arxiv-2409.11990","DOIUrl":null,"url":null,"abstract":"In this study, we propose high-order implicit and semi-implicit schemes for\nsolving ordinary differential equations (ODEs) based on Taylor series\nexpansion. These methods are designed to handle stiff and non-stiff components\nwithin a unified framework, ensuring stability and accuracy. The schemes are\nderived and analyzed for their consistency and stability properties, showcasing\ntheir effectiveness in practical computational scenarios.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"204 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations\",\"authors\":\"S. Boscarino, E. Macca\",\"doi\":\"arxiv-2409.11990\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, we propose high-order implicit and semi-implicit schemes for\\nsolving ordinary differential equations (ODEs) based on Taylor series\\nexpansion. These methods are designed to handle stiff and non-stiff components\\nwithin a unified framework, ensuring stability and accuracy. The schemes are\\nderived and analyzed for their consistency and stability properties, showcasing\\ntheir effectiveness in practical computational scenarios.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"204 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11990\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11990","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在本研究中，我们提出了基于泰勒级数展开的高阶隐式和半隐式常微分方程求解方案。这些方法旨在统一框架内处理刚性和非刚性成分，确保稳定性和准确性。对这些方案的一致性和稳定性进行了计算和分析，展示了它们在实际计算场景中的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a unified framework, ensuring stability and accuracy. The schemes are derived and analyzed for their consistency and stability properties, showcasing their effectiveness in practical computational scenarios.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Numerical Analysis

自引率

0.00%

发文量