Existence of the unsteady heat conduction in Sobolev space and numerical technique with twenty-one global nodes

Mohamad Tafrikan, Yolanda Norasia, Mohammad Ghani

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We are interested in the existence of unsteady heat conduction in Sobolev space by using the Littlewood-Paley decomposition and also Gronwall inequality to establish the uniqueness of the solution. We further consider one-dimensional unsteady-state heat conduction to make an easy numerical technique. Furthermore, this Equation is discretized as 20 subdomains to obtain 20 elements and 21 nodes called global nodes. Every global node consists of element nodes having the same basis function for all element nodes. These all element nodes will be assembled to be a global stiffness matrix with 21 unknown temperature values for each iteration of time. The homotopy perturbation method is then used to approximate the analytic solution to one-dimensional unsteady heat conduction.

Original languageEnglish
Title of host publicationProceedings of the 6th National Conference on Mathematics and Mathematics Education, SENATIK 2021
Editors Sutrisno, Muhtarom, Dewi Wulandari, Nurina Happy, Ali Shodiqin, Yanuar Hery Murtianto, Kartinah
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735443600
DOIs
Publication statusPublished - 13 Jul 2022
Event6th National Conference on Mathematics and Mathematics Education, SENATIK 2021 - Semarang, Indonesia
Duration: 11 Aug 2021 → …

Publication series

NameAIP Conference Proceedings
Volume2577
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference6th National Conference on Mathematics and Mathematics Education, SENATIK 2021
Country/TerritoryIndonesia
CitySemarang
Period11/08/21 → …

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