{"title":"用于 ODEs 的 A 稳定双衍单隐式 Runge-Kutta 方法","authors":"I. B. Aihie, R. Okuonghae","doi":"10.34198/ejms.14324.565588","DOIUrl":null,"url":null,"abstract":"An A-stable Two Derivative Mono Implicit Runge-Kutta (ATDMIRK) method is considered herein for the numerical solution of initial value problems (IVPs) in ordinary differential equation (ODEs). The methods are of high-order A-stable for $p=q=\\lbrace 2s+1\\rbrace _{s=2}^{7}\\ $ The $p$, $q$ and $s$ are the order of the input, output and the stages of the methods respectively. The numerical results affirm the superior accuracy of the newly develop methods compare to the existing ones.","PeriodicalId":482741,"journal":{"name":"Earthline Journal of Mathematical Sciences","volume":"71 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEs\",\"authors\":\"I. B. Aihie, R. Okuonghae\",\"doi\":\"10.34198/ejms.14324.565588\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An A-stable Two Derivative Mono Implicit Runge-Kutta (ATDMIRK) method is considered herein for the numerical solution of initial value problems (IVPs) in ordinary differential equation (ODEs). The methods are of high-order A-stable for $p=q=\\\\lbrace 2s+1\\\\rbrace _{s=2}^{7}\\\\ $ The $p$, $q$ and $s$ are the order of the input, output and the stages of the methods respectively. The numerical results affirm the superior accuracy of the newly develop methods compare to the existing ones.\",\"PeriodicalId\":482741,\"journal\":{\"name\":\"Earthline Journal of Mathematical Sciences\",\"volume\":\"71 5\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Earthline Journal of Mathematical Sciences\",\"FirstCategoryId\":\"0\",\"ListUrlMain\":\"https://doi.org/10.34198/ejms.14324.565588\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Earthline Journal of Mathematical Sciences","FirstCategoryId":"0","ListUrlMain":"https://doi.org/10.34198/ejms.14324.565588","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
本文研究了一种 A 级稳定的二阶微分单隐式 Runge-Kutta (ATDMIRK) 方法，用于常微分方程中初值问题的数值求解。这些方法在 $p=q=\lbrace 2s+1\rbrace _{s=2}^{7}\ $ 时具有高阶 A 级稳定性。数值结果表明，与现有方法相比，新开发的方法具有更高的精度。
A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEs
An A-stable Two Derivative Mono Implicit Runge-Kutta (ATDMIRK) method is considered herein for the numerical solution of initial value problems (IVPs) in ordinary differential equation (ODEs). The methods are of high-order A-stable for $p=q=\lbrace 2s+1\rbrace _{s=2}^{7}\ $ The $p$, $q$ and $s$ are the order of the input, output and the stages of the methods respectively. The numerical results affirm the superior accuracy of the newly develop methods compare to the existing ones.
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