{"title":"半线性子扩散方程分级网格上的 L2 型方法误差分析","authors":"Natalia Kopteva","doi":"10.1016/j.aml.2024.109306","DOIUrl":null,"url":null,"abstract":"<div><p>A semilinear initial–boundary value problem with a Caputo time derivative of fractional order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order <span><math><mrow><mn>3</mn><mo>−</mo><mi>α</mi></mrow></math></span>, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109306"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0893965924003264/pdfft?md5=6e39bf3f9038caa96e147fc377174a7a&pid=1-s2.0-S0893965924003264-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations\",\"authors\":\"Natalia Kopteva\",\"doi\":\"10.1016/j.aml.2024.109306\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A semilinear initial–boundary value problem with a Caputo time derivative of fractional order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order <span><math><mrow><mn>3</mn><mo>−</mo><mi>α</mi></mrow></math></span>, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"160 \",\"pages\":\"Article 109306\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0893965924003264/pdfft?md5=6e39bf3f9038caa96e147fc377174a7a&pid=1-s2.0-S0893965924003264-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924003264\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003264","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations
A semilinear initial–boundary value problem with a Caputo time derivative of fractional order is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order , we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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