{"title":"Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations","authors":"Charles Wing Ho Green, Yubin Yan","doi":"10.3390/foundations2040057","DOIUrl":null,"url":null,"abstract":"We consider a predictor–corrector numerical method for solving Caputo–Hadamard fractional differential equation over the uniform mesh logtj=loga+logtNajN,j=0,1,2,…,N with a≥1, where loga=logt0<logt1<…<logtN=logT is a partition of [loga,logT]. The error estimates under the different smoothness properties of the solution y and the nonlinear function f are studied. Numerical examples are given to verify that the numerical results are consistent with the theoretical results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"53 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/foundations2040057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We consider a predictor–corrector numerical method for solving Caputo–Hadamard fractional differential equation over the uniform mesh logtj=loga+logtNajN,j=0,1,2,…,N with a≥1, where loga=logt0