{"title":"Error estimates of implicit-explicit compact BDF2 schemes for the pseudo parabolic equations with logarithmic nonlinearity","authors":"Qifeng Zhang , Haiyan Cao , Hongyu Qin","doi":"10.1016/j.apnum.2025.01.010","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, two classes of linearized difference schemes are presented for the one and two-dimensional pseudo parabolic equations with logarithmic nonlinearity. These schemes are derived based on the implicit-explicit second-order backward differential formula (BDF2) for the temporal discretization and fourth-order compact/second-order difference schemes for spatial discretization. With the help of the truncation function method and regularization technique, error estimates for the logarithmic nonlinear term are handled rigorously. As a result, the convergence of the fully-discrete schemes is obtained based on the energy argument. Extensive numerical examples are presented to confirm the theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 135-154"},"PeriodicalIF":2.4000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927425000108","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, two classes of linearized difference schemes are presented for the one and two-dimensional pseudo parabolic equations with logarithmic nonlinearity. These schemes are derived based on the implicit-explicit second-order backward differential formula (BDF2) for the temporal discretization and fourth-order compact/second-order difference schemes for spatial discretization. With the help of the truncation function method and regularization technique, error estimates for the logarithmic nonlinear term are handled rigorously. As a result, the convergence of the fully-discrete schemes is obtained based on the energy argument. Extensive numerical examples are presented to confirm the theoretical results.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
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(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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