Loading…

Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states

The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be...

Full description

Saved in:
Bibliographic Details
Published in:Numerische Mathematik 2020-11, Vol.146 (3), p.481-511
Main Authors: Nie, Daxin, Sun, Jing, Deng, Weihua
Format: Article
Language:English
Subjects:
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-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3
cites cdi_FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3
container_end_page 511
container_issue 3
container_start_page 481
container_title Numerische Mathematik
container_volume 146
creator Nie, Daxin
Sun, Jing
Deng, Weihua
description The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two-state Fokker–Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use L 1 scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by one- and two-dimensional numerical experiments.
doi_str_mv 10.1007/s00211-020-01148-6
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2473792168</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2473792168</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3</originalsourceid><addsrcrecordid>eNp9kMtKAzEUQIMoWKs_4CrgOprHJJkspVgVirpQcBcymaSddqapSYp05z_4h36JU0dw5-rexTmXywHgnOBLgrG8ShhTQhCmGGFCihKJAzDCquCI0YIf9jumCnGlXo_BSUpLjIkUBRkB87DtXGysaaFp5yE2edFBHyLMCwfTxliHctM56KOxuQnrnpuG1crFr4_Pp9as7QqmXcqug--9CvN7gM06u7gHUzbZpVNw5E2b3NnvHIOX6c3z5A7NHm_vJ9czZBlRGRnFvKfWVqq2VSm4s0wVlFfCC1tTaXxdccdEiY2XlntWCylVRZUpBLfW1GwMLoa7mxjeti5lvQzb_R9J00IyqSgRZU_RgbIxpBSd15vYdCbuNMF6n1IPKXWfUv-k1KKX2CClHl7PXfw7_Y_1DQDCehU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2473792168</pqid></control><display><type>article</type><title>Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states</title><source>Springer Nature</source><creator>Nie, Daxin ; Sun, Jing ; Deng, Weihua</creator><creatorcontrib>Nie, Daxin ; Sun, Jing ; Deng, Weihua</creatorcontrib><description>The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two-state Fokker–Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use L 1 scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by one- and two-dimensional numerical experiments.</description><identifier>ISSN: 0029-599X</identifier><identifier>EISSN: 0945-3245</identifier><identifier>DOI: 10.1007/s00211-020-01148-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Approximation ; Finite element method ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Numerical and Computational Physics ; Operators (mathematics) ; Regularity ; Simulation ; Theoretical</subject><ispartof>Numerische Mathematik, 2020-11, Vol.146 (3), p.481-511</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3</citedby><cites>FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids></links><search><creatorcontrib>Nie, Daxin</creatorcontrib><creatorcontrib>Sun, Jing</creatorcontrib><creatorcontrib>Deng, Weihua</creatorcontrib><title>Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states</title><title>Numerische Mathematik</title><addtitle>Numer. Math</addtitle><description>The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two-state Fokker–Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use L 1 scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by one- and two-dimensional numerical experiments.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Finite element method</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Numerical and Computational Physics</subject><subject>Operators (mathematics)</subject><subject>Regularity</subject><subject>Simulation</subject><subject>Theoretical</subject><issn>0029-599X</issn><issn>0945-3245</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUQIMoWKs_4CrgOprHJJkspVgVirpQcBcymaSddqapSYp05z_4h36JU0dw5-rexTmXywHgnOBLgrG8ShhTQhCmGGFCihKJAzDCquCI0YIf9jumCnGlXo_BSUpLjIkUBRkB87DtXGysaaFp5yE2edFBHyLMCwfTxliHctM56KOxuQnrnpuG1crFr4_Pp9as7QqmXcqug--9CvN7gM06u7gHUzbZpVNw5E2b3NnvHIOX6c3z5A7NHm_vJ9czZBlRGRnFvKfWVqq2VSm4s0wVlFfCC1tTaXxdccdEiY2XlntWCylVRZUpBLfW1GwMLoa7mxjeti5lvQzb_R9J00IyqSgRZU_RgbIxpBSd15vYdCbuNMF6n1IPKXWfUv-k1KKX2CClHl7PXfw7_Y_1DQDCehU</recordid><startdate>20201101</startdate><enddate>20201101</enddate><creator>Nie, Daxin</creator><creator>Sun, Jing</creator><creator>Deng, Weihua</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201101</creationdate><title>Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states</title><author>Nie, Daxin ; Sun, Jing ; Deng, Weihua</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Finite element method</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Numerical and Computational Physics</topic><topic>Operators (mathematics)</topic><topic>Regularity</topic><topic>Simulation</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nie, Daxin</creatorcontrib><creatorcontrib>Sun, Jing</creatorcontrib><creatorcontrib>Deng, Weihua</creatorcontrib><collection>CrossRef</collection><jtitle>Numerische Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nie, Daxin</au><au>Sun, Jing</au><au>Deng, Weihua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states</atitle><jtitle>Numerische Mathematik</jtitle><stitle>Numer. Math</stitle><date>2020-11-01</date><risdate>2020</risdate><volume>146</volume><issue>3</issue><spage>481</spage><epage>511</epage><pages>481-511</pages><issn>0029-599X</issn><eissn>0945-3245</eissn><abstract>The fractional Fokker–Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., 13 , 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two-state Fokker–Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use L 1 scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by one- and two-dimensional numerical experiments.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00211-020-01148-6</doi><tpages>31</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0029-599X
ispartof Numerische Mathematik, 2020-11, Vol.146 (3), p.481-511
issn 0029-599X
0945-3245
language eng
recordid cdi_proquest_journals_2473792168
source Springer Nature
subjects Algorithms
Approximation
Finite element method
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Operators (mathematics)
Regularity
Simulation
Theoretical
title Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T18%3A01%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Numerical%20algorithm%20for%20the%20space-time%20fractional%20Fokker%E2%80%93Planck%20system%20with%20two%20internal%20states&rft.jtitle=Numerische%20Mathematik&rft.au=Nie,%20Daxin&rft.date=2020-11-01&rft.volume=146&rft.issue=3&rft.spage=481&rft.epage=511&rft.pages=481-511&rft.issn=0029-599X&rft.eissn=0945-3245&rft_id=info:doi/10.1007/s00211-020-01148-6&rft_dat=%3Cproquest_cross%3E2473792168%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-a93ff2ccb9dcb865ec39425b6f6cd27afdb5e3680af7c5f3d6779b29a465ccad3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2473792168&rft_id=info:pmid/&rfr_iscdi=true