{"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}
引用次数: 0
Abstract
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.