Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative

This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional d...

Full description

Saved in:
Bibliographic Details
Published in:Arabian journal of mathematics 2024-08, Vol.13 (2), p.409-424
Main Authors: Singh, Harvindra, Mittal, A. K., Balyan, L. K.
Format: Article
Language:English
Subjects:
35C11
35G31
35R11
65M70
Burgers equation
Chebyshev approximation
Error analysis
Exact solutions
Finite volume method
Mathematics
Mathematics and Statistics
Nonlinear equations
Partial differential equations
Reynolds number
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c339t-847881fbcab4a35bcdde855498944c4c5dcc838567d3bbbc24199de33ff6a7743
container_end_page 424
container_issue 2
container_start_page 409
container_title Arabian journal of mathematics
container_volume 13
creator Singh, Harvindra
Mittal, A. K.
Balyan, L. K.
description This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of ν is done for various model examples of fractional Burgers equations, where ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.
doi_str_mv 10.1007/s40065-024-00465-0
format article
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_9c1f0446f11d49f68b687f455a1d2268</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_9c1f0446f11d49f68b687f455a1d2268</doaj_id><sourcerecordid>3093003891</sourcerecordid><originalsourceid>FETCH-LOGICAL-c339t-847881fbcab4a35bcdde855498944c4c5dcc838567d3bbbc24199de33ff6a7743</originalsourceid><addsrcrecordid>eNp9kUtPwzAQhCMEEqjwBzhF4hxYZ-3EPkLFo1IlOMDZcvxAqdK4tZNK_fe4BBVOnDxafzMre7LsmsAtAajvIgWoWAElLQDoQZ1kFyURWDBk5PSoKZ5nVzGuAIAAwxrJRda_RTsaHzdWD0F1uepVt49tzJ0P-Xrshta0a9vH1qeL3AWlh0k-jOHThpjb7agOo7xR0Zo8ibnajIP_yxob2l2idvYyO3Oqi_bq55xlH0-P7_OXYvn6vJjfLwuNKIaC05pz4hqtGqqQNdoYyxmjggtKNdXMaM2Rs6o22DSNLikRwlhE5ypV1xRn2WLKNV6t5Ca0axX20qtWfg98-JQqDK3urBSaOKC0coQYKlzFm4rXjjKmiCnLiqesmylrE_x2tHGQKz-G9K4oEQQCIBckUeVE6eBjDNYdtxKQh5rkVJNMNcnvmiQkE06mmOA-_edv9D-uLyFNltM</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3093003891</pqid></control><display><type>article</type><title>Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative</title><source>Publicly Available Content Database</source><source>Springer Nature - SpringerLink Journals - Fully Open Access </source><creator>Singh, Harvindra ; Mittal, A. K. ; Balyan, L. K.</creator><creatorcontrib>Singh, Harvindra ; Mittal, A. K. ; Balyan, L. K.</creatorcontrib><description>This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of ν is done for various model examples of fractional Burgers equations, where ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.</description><identifier>ISSN: 2193-5343</identifier><identifier>ISSN: 2193-5351</identifier><identifier>EISSN: 2193-5351</identifier><identifier>DOI: 10.1007/s40065-024-00465-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>35C11 ; 35G31 ; 35R11 ; 65M70 ; Burgers equation ; Chebyshev approximation ; Error analysis ; Exact solutions ; Finite volume method ; Mathematics ; Mathematics and Statistics ; Nonlinear equations ; Partial differential equations ; Reynolds number</subject><ispartof>Arabian journal of mathematics, 2024-08, Vol.13 (2), p.409-424</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c339t-847881fbcab4a35bcdde855498944c4c5dcc838567d3bbbc24199de33ff6a7743</cites><orcidid>0000-0003-1695-2658</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/3093003891/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/3093003891?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25751,27922,27923,37010,44588,74896</link.rule.ids></links><search><creatorcontrib>Singh, Harvindra</creatorcontrib><creatorcontrib>Mittal, A. K.</creatorcontrib><creatorcontrib>Balyan, L. K.</creatorcontrib><title>Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative</title><title>Arabian journal of mathematics</title><addtitle>Arab. J. Math</addtitle><description>This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of ν is done for various model examples of fractional Burgers equations, where ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.</description><subject>35C11</subject><subject>35G31</subject><subject>35R11</subject><subject>65M70</subject><subject>Burgers equation</subject><subject>Chebyshev approximation</subject><subject>Error analysis</subject><subject>Exact solutions</subject><subject>Finite volume method</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear equations</subject><subject>Partial differential equations</subject><subject>Reynolds number</subject><issn>2193-5343</issn><issn>2193-5351</issn><issn>2193-5351</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp9kUtPwzAQhCMEEqjwBzhF4hxYZ-3EPkLFo1IlOMDZcvxAqdK4tZNK_fe4BBVOnDxafzMre7LsmsAtAajvIgWoWAElLQDoQZ1kFyURWDBk5PSoKZ5nVzGuAIAAwxrJRda_RTsaHzdWD0F1uepVt49tzJ0P-Xrshta0a9vH1qeL3AWlh0k-jOHThpjb7agOo7xR0Zo8ibnajIP_yxob2l2idvYyO3Oqi_bq55xlH0-P7_OXYvn6vJjfLwuNKIaC05pz4hqtGqqQNdoYyxmjggtKNdXMaM2Rs6o22DSNLikRwlhE5ypV1xRn2WLKNV6t5Ca0axX20qtWfg98-JQqDK3urBSaOKC0coQYKlzFm4rXjjKmiCnLiqesmylrE_x2tHGQKz-G9K4oEQQCIBckUeVE6eBjDNYdtxKQh5rkVJNMNcnvmiQkE06mmOA-_edv9D-uLyFNltM</recordid><startdate>20240801</startdate><enddate>20240801</enddate><creator>Singh, Harvindra</creator><creator>Mittal, A. K.</creator><creator>Balyan, L. K.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</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>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-1695-2658</orcidid></search><sort><creationdate>20240801</creationdate><title>Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative</title><author>Singh, Harvindra ; Mittal, A. K. ; Balyan, L. K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-847881fbcab4a35bcdde855498944c4c5dcc838567d3bbbc24199de33ff6a7743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>35C11</topic><topic>35G31</topic><topic>35R11</topic><topic>65M70</topic><topic>Burgers equation</topic><topic>Chebyshev approximation</topic><topic>Error analysis</topic><topic>Exact solutions</topic><topic>Finite volume method</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear equations</topic><topic>Partial differential equations</topic><topic>Reynolds number</topic><toplevel>online_resources</toplevel><creatorcontrib>Singh, Harvindra</creatorcontrib><creatorcontrib>Mittal, A. K.</creatorcontrib><creatorcontrib>Balyan, L. K.</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</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>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Arabian journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Singh, Harvindra</au><au>Mittal, A. K.</au><au>Balyan, L. K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative</atitle><jtitle>Arabian journal of mathematics</jtitle><stitle>Arab. J. Math</stitle><date>2024-08-01</date><risdate>2024</risdate><volume>13</volume><issue>2</issue><spage>409</spage><epage>424</epage><pages>409-424</pages><issn>2193-5343</issn><issn>2193-5351</issn><eissn>2193-5351</eissn><abstract>This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of ν is done for various model examples of fractional Burgers equations, where ν represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40065-024-00465-0</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0003-1695-2658</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2193-5343
ispartof Arabian journal of mathematics, 2024-08, Vol.13 (2), p.409-424
issn 2193-5343
2193-5351
2193-5351
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_9c1f0446f11d49f68b687f455a1d2268
source Publicly Available Content Database; Springer Nature - SpringerLink Journals - Fully Open Access
subjects 35C11
35G31
35R11
65M70
Burgers equation
Chebyshev approximation
Error analysis
Exact solutions
Finite volume method
Mathematics
Mathematics and Statistics
Nonlinear equations
Partial differential equations
Reynolds number
title Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-13T21%3A45%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Pseudospectral%20analysis%20for%20multidimensional%20fractional%20Burgers%20equation%20based%20on%20Caputo%20fractional%20derivative&rft.jtitle=Arabian%20journal%20of%20mathematics&rft.au=Singh,%20Harvindra&rft.date=2024-08-01&rft.volume=13&rft.issue=2&rft.spage=409&rft.epage=424&rft.pages=409-424&rft.issn=2193-5343&rft.eissn=2193-5351&rft_id=info:doi/10.1007/s40065-024-00465-0&rft_dat=%3Cproquest_doaj_%3E3093003891%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c339t-847881fbcab4a35bcdde855498944c4c5dcc838567d3bbbc24199de33ff6a7743%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=3093003891&rft_id=info:pmid/&rfr_iscdi=true