拟线性次扩散方程的线性正则化有限差分格式

Pub Date : 2022-08-01 DOI:10.1515/rnam-2022-0019
A. Lapin, E. Laitinen
{"title":"拟线性次扩散方程的线性正则化有限差分格式","authors":"A. Lapin, E. Laitinen","doi":"10.1515/rnam-2022-0019","DOIUrl":null,"url":null,"abstract":"Abstract A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear regularized finite difference scheme for the quasilinear subdiffusion equation\",\"authors\":\"A. Lapin, E. Laitinen\",\"doi\":\"10.1515/rnam-2022-0019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/rnam-2022-0019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/rnam-2022-0019","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

摘要考虑一类导数为时间分数阶的拟线性抛物方程的齐次Dirichlet初边值问题,椭圆部分的系数依赖于解的梯度。系数的条件保证了椭圆算子在梯度在空间变量上一致有界的函数集合上的单调性和Lipschitz性质。针对这一问题,构造并研究了线性正则化网格格式。导出了保证网格方案局部正确性的正则化参数的充分条件。在时间分数Caputo或Caputo - fabrizio导数模型问题的正确性和近似估计的基础上,在微分问题光滑解存在的假设下,给出了基于网格和正则化参数的精度估计。给出的数值实验结果证实了所得到的渐近精度估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
Linear regularized finite difference scheme for the quasilinear subdiffusion equation
Abstract A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1