A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials

The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polyno...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry (Basel) 2023-03, Vol.15 (3), p.594
Main Authors: Abdelghany, Esraa Magdy, Abd-Elhameed, Waleed Mohamed, Moatimid, Galal Mahrous, Youssri, Youssri Hassan, Atta, Ahmed Gamal
Format: Article
Language:English
Subjects:
Basis functions
Calculus
Chebyshev approximation
Chebyshev polynomials of the sixth-kind
Error analysis
Fourier transforms
Linear algebra
Mathematical analysis
Methods
Partial differential equations
Polynomials
tau method
Temperature
Thermodynamics
time fractional heat equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3
cites cdi_FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3
container_end_page
container_issue 3
container_start_page 594
container_title Symmetry (Basel)
container_volume 15
creator Abdelghany, Esraa Magdy
Abd-Elhameed, Waleed Mohamed
Moatimid, Galal Mahrous
Youssri, Youssri Hassan
Atta, Ahmed Gamal
description The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.
doi_str_mv 10.3390/sym15030594
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_e1b3b5d1a527416f968ad2d0c75072b4</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A752149387</galeid><doaj_id>oai_doaj_org_article_e1b3b5d1a527416f968ad2d0c75072b4</doaj_id><sourcerecordid>A752149387</sourcerecordid><originalsourceid>FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3</originalsourceid><addsrcrecordid>eNpNUU1rGzEQXUoLDUlO_QOCHsumo6_V6uiapAkJtGD3LPTpldldOdI61P--Sl1KZg5vZnjzkN40zScMN5RK-FpOE-ZAgUv2rrkgIGjbS8nev6k_Ntel7KEGB846uGjmFdrqI1odDjlpO6CQMtqk8SXOO7SNk2_vsrZLTLMe0b3XC7p9PurXHn3TxTtUi2XwaDPEsNR2E38vQ_sYZ4fWgzenMvgX9DONpzlNUY_lqvkQKvjrf3jZ_Lq73a7v26cf3x_Wq6fWMqBLy6imvTBcSIMNCz1gq52xFFviicQMguwodgEM6YBIkF1FHyQlFPMeNL1sHs66Lum9OuQ46XxSSUf1d5DyTum8RDt65bGhhjusOREMd1W51444sIKDIIZVrc9nrWrR89GXRe3TMVdDiiJCYgGYSVFZN2fWTlfROIe0VOdqOj9Fm2YfYp2vBCeVXj9XF76cF2xOpWQf_j8Tg3o9qHpzUPoHlWWQtA</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2791701497</pqid></control><display><type>article</type><title>A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials</title><source>Publicly Available Content Database (Proquest) (PQ_SDU_P3)</source><creator>Abdelghany, Esraa Magdy ; Abd-Elhameed, Waleed Mohamed ; Moatimid, Galal Mahrous ; Youssri, Youssri Hassan ; Atta, Ahmed Gamal</creator><creatorcontrib>Abdelghany, Esraa Magdy ; Abd-Elhameed, Waleed Mohamed ; Moatimid, Galal Mahrous ; Youssri, Youssri Hassan ; Atta, Ahmed Gamal</creatorcontrib><description>The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.</description><identifier>ISSN: 2073-8994</identifier><identifier>EISSN: 2073-8994</identifier><identifier>DOI: 10.3390/sym15030594</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Basis functions ; Calculus ; Chebyshev approximation ; Chebyshev polynomials of the sixth-kind ; Error analysis ; Fourier transforms ; Linear algebra ; Mathematical analysis ; Methods ; Partial differential equations ; Polynomials ; tau method ; Temperature ; Thermodynamics ; time fractional heat equation</subject><ispartof>Symmetry (Basel), 2023-03, Vol.15 (3), p.594</ispartof><rights>COPYRIGHT 2023 MDPI AG</rights><rights>2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3</citedby><cites>FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3</cites><orcidid>0000-0003-0403-8797 ; 0000-0001-6833-8903 ; 0000-0003-1467-640X ; 0000-0001-9516-884X ; 0000-0002-6102-671X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2791701497/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2791701497?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590,75126</link.rule.ids></links><search><creatorcontrib>Abdelghany, Esraa Magdy</creatorcontrib><creatorcontrib>Abd-Elhameed, Waleed Mohamed</creatorcontrib><creatorcontrib>Moatimid, Galal Mahrous</creatorcontrib><creatorcontrib>Youssri, Youssri Hassan</creatorcontrib><creatorcontrib>Atta, Ahmed Gamal</creatorcontrib><title>A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials</title><title>Symmetry (Basel)</title><description>The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.</description><subject>Basis functions</subject><subject>Calculus</subject><subject>Chebyshev approximation</subject><subject>Chebyshev polynomials of the sixth-kind</subject><subject>Error analysis</subject><subject>Fourier transforms</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Methods</subject><subject>Partial differential equations</subject><subject>Polynomials</subject><subject>tau method</subject><subject>Temperature</subject><subject>Thermodynamics</subject><subject>time fractional heat equation</subject><issn>2073-8994</issn><issn>2073-8994</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpNUU1rGzEQXUoLDUlO_QOCHsumo6_V6uiapAkJtGD3LPTpldldOdI61P--Sl1KZg5vZnjzkN40zScMN5RK-FpOE-ZAgUv2rrkgIGjbS8nev6k_Ntel7KEGB846uGjmFdrqI1odDjlpO6CQMtqk8SXOO7SNk2_vsrZLTLMe0b3XC7p9PurXHn3TxTtUi2XwaDPEsNR2E38vQ_sYZ4fWgzenMvgX9DONpzlNUY_lqvkQKvjrf3jZ_Lq73a7v26cf3x_Wq6fWMqBLy6imvTBcSIMNCz1gq52xFFviicQMguwodgEM6YBIkF1FHyQlFPMeNL1sHs66Lum9OuQ46XxSSUf1d5DyTum8RDt65bGhhjusOREMd1W51444sIKDIIZVrc9nrWrR89GXRe3TMVdDiiJCYgGYSVFZN2fWTlfROIe0VOdqOj9Fm2YfYp2vBCeVXj9XF76cF2xOpWQf_j8Tg3o9qHpzUPoHlWWQtA</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Abdelghany, Esraa Magdy</creator><creator>Abd-Elhameed, Waleed Mohamed</creator><creator>Moatimid, Galal Mahrous</creator><creator>Youssri, Youssri Hassan</creator><creator>Atta, Ahmed Gamal</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-0403-8797</orcidid><orcidid>https://orcid.org/0000-0001-6833-8903</orcidid><orcidid>https://orcid.org/0000-0003-1467-640X</orcidid><orcidid>https://orcid.org/0000-0001-9516-884X</orcidid><orcidid>https://orcid.org/0000-0002-6102-671X</orcidid></search><sort><creationdate>20230301</creationdate><title>A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials</title><author>Abdelghany, Esraa Magdy ; Abd-Elhameed, Waleed Mohamed ; Moatimid, Galal Mahrous ; Youssri, Youssri Hassan ; Atta, Ahmed Gamal</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Basis functions</topic><topic>Calculus</topic><topic>Chebyshev approximation</topic><topic>Chebyshev polynomials of the sixth-kind</topic><topic>Error analysis</topic><topic>Fourier transforms</topic><topic>Linear algebra</topic><topic>Mathematical analysis</topic><topic>Methods</topic><topic>Partial differential equations</topic><topic>Polynomials</topic><topic>tau method</topic><topic>Temperature</topic><topic>Thermodynamics</topic><topic>time fractional heat equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abdelghany, Esraa Magdy</creatorcontrib><creatorcontrib>Abd-Elhameed, Waleed Mohamed</creatorcontrib><creatorcontrib>Moatimid, Galal Mahrous</creatorcontrib><creatorcontrib>Youssri, Youssri Hassan</creatorcontrib><creatorcontrib>Atta, Ahmed Gamal</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Symmetry (Basel)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abdelghany, Esraa Magdy</au><au>Abd-Elhameed, Waleed Mohamed</au><au>Moatimid, Galal Mahrous</au><au>Youssri, Youssri Hassan</au><au>Atta, Ahmed Gamal</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials</atitle><jtitle>Symmetry (Basel)</jtitle><date>2023-03-01</date><risdate>2023</risdate><volume>15</volume><issue>3</issue><spage>594</spage><pages>594-</pages><issn>2073-8994</issn><eissn>2073-8994</eissn><abstract>The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/sym15030594</doi><orcidid>https://orcid.org/0000-0003-0403-8797</orcidid><orcidid>https://orcid.org/0000-0001-6833-8903</orcidid><orcidid>https://orcid.org/0000-0003-1467-640X</orcidid><orcidid>https://orcid.org/0000-0001-9516-884X</orcidid><orcidid>https://orcid.org/0000-0002-6102-671X</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2073-8994
ispartof Symmetry (Basel), 2023-03, Vol.15 (3), p.594
issn 2073-8994
2073-8994
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_e1b3b5d1a527416f968ad2d0c75072b4
source Publicly Available Content Database (Proquest) (PQ_SDU_P3)
subjects Basis functions
Calculus
Chebyshev approximation
Chebyshev polynomials of the sixth-kind
Error analysis
Fourier transforms
Linear algebra
Mathematical analysis
Methods
Partial differential equations
Polynomials
tau method
Temperature
Thermodynamics
time fractional heat equation
title A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T17%3A24%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Tau%20Approach%20for%20Solving%20Time-Fractional%20Heat%20Equation%20Based%20on%20the%20Shifted%20Sixth-Kind%20Chebyshev%20Polynomials&rft.jtitle=Symmetry%20(Basel)&rft.au=Abdelghany,%20Esraa%20Magdy&rft.date=2023-03-01&rft.volume=15&rft.issue=3&rft.spage=594&rft.pages=594-&rft.issn=2073-8994&rft.eissn=2073-8994&rft_id=info:doi/10.3390/sym15030594&rft_dat=%3Cgale_doaj_%3EA752149387%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c403t-43a387b579b1b4f801cadbc31c2e29140f9631df0b26029096260ef93231580a3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2791701497&rft_id=info:pmid/&rft_galeid=A752149387&rfr_iscdi=true