{"title":"Caputo-Hadamard分数阶微分方程分数阶Adams方法的详细误差分析","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":"{\"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}","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}
Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations
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
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