A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators

The main aim of this article is to analyze the efficiency of general solvers for parabolic problems with fractional power elliptic operators. Such discrete schemes can be used in the cases of non-constant elliptic operators, non-uniform space meshes and general space domains. The stability results a...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Mathematics (Basel) Ročník 9; číslo 12; s. 1344
Hlavní autori:	Čiegis, Raimondas, Čiegis, Remigijus, Dapšys, Ignas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.06.2021
Predmet:	Algorithms Approximation Boundary conditions Calculus discrete schemes Dynamical systems Food science fractional power elliptic operators Investigations Methods nonlinear diffusion-reaction Operators parabolic equations Splitting splitting methods stability
ISSN:	2227-7390, 2227-7390
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	The main aim of this article is to analyze the efficiency of general solvers for parabolic problems with fractional power elliptic operators. Such discrete schemes can be used in the cases of non-constant elliptic operators, non-uniform space meshes and general space domains. The stability results are proved for all algorithms and the accuracy of obtained approximations is estimated by solving well-known test problems. A modification of the second order splitting scheme is presented, it combines the splitting method to solve locally the nonlinear subproblem and the AAA algorithm to solve the nonlocal diffusion subproblem. Results of computational experiments are presented and analyzed.
AbstractList	The main aim of this article is to analyze the efficiency of general solvers for parabolic problems with fractional power elliptic operators. Such discrete schemes can be used in the cases of non-constant elliptic operators, non-uniform space meshes and general space domains. The stability results are proved for all algorithms and the accuracy of obtained approximations is estimated by solving well-known test problems. A modification of the second order splitting scheme is presented, it combines the splitting method to solve locally the nonlinear subproblem and the AAA algorithm to solve the nonlocal diffusion subproblem. Results of computational experiments are presented and analyzed.
Author	Dapšys, Ignas Čiegis, Remigijus Čiegis, Raimondas
Author_xml	– sequence: 1 givenname: Raimondas surname: Čiegis fullname: Čiegis, Raimondas – sequence: 2 givenname: Remigijus surname: Čiegis fullname: Čiegis, Remigijus – sequence: 3 givenname: Ignas surname: Dapšys fullname: Dapšys, Ignas
BookMark	eNptkUtrGzEQx0VIIWmaU7-AIMfiVq9d7R6DG7eB0BjSnsWsVopltNZ2JCfk21euWwilc5kHv_kzj7fkdJd2jpD3nH2UsmefJiibngsulToh50IIvdC1fvoqPiOXOW9ZtZ7LTvXn5OmaLtM0A4acdjR5-jlki644-mA3bnKZ-oT0235yGCxE-pDivoQjugaEIcVg6RrTEN2U6XMoG7pCsAem4uv07JDexBjmUrn72SGUhPkdeeMhZnf5x1-QH6ub78uvi7v7L7fL67uFla0qi7pLr4UdfDdq76VyUgIfLOMdDBY0H5VXg1Qw9txDa0cQNedyEAC601LKC3J71B0TbM2MYQJ8MQmC-V1I-GgA62TRGfB6VK7twLNWCdsM2raqcd4Jxixvuqp1ddSaMf3cu1zMNu2xbpmNaFTDWMNbXSl-pCymnNF5Y0OBwzkKQoiGM3P4lnn1rdrz4Z-ev5P-j_4FtASZqA
CitedBy_id	crossref_primary_10_3390_axioms11030098 crossref_primary_10_1007_s13540_024_00256_6 crossref_primary_10_3390_fractalfract5030061 crossref_primary_10_3390_math10132155 crossref_primary_10_3846_mma_2023_17583
Cites_doi	10.1140/epjb/e20020151 10.1137/100800634 10.1016/j.cam.2017.09.007 10.1016/j.jcp.2019.109141 10.1002/cpe.5163 10.1126/science.1088172 10.1007/s10208-018-9402-3 10.1090/S0025-5718-2015-02937-8 10.1201/b19666 10.1016/j.cam.2019.112627 10.1016/j.chaos.2009.04.002 10.1007/s00211-019-01055-5 10.1029/2000WR900409 10.1016/j.apnum.2021.03.006 10.1016/S0006-3495(01)75870-5 10.1088/0305-4470/37/31/R01 10.1016/j.cam.2016.06.020 10.1016/j.apm.2014.02.005 10.1007/s10955-018-2116-8 10.1137/16M1106122 10.15388/NA.2018.3.9 10.1016/j.chaos.2018.07.033 10.1093/imanum/drz054 10.1016/j.jcp.2005.12.006 10.1007/s10543-014-0484-2 10.1016/j.jcp.2005.08.008 10.1007/978-3-642-14003-7 10.1016/j.camwa.2019.07.025 10.1016/j.camwa.2019.08.012 10.1016/j.aml.2008.06.003 10.1002/nla.2167 10.1007/s10208-014-9208-x 10.1098/rsif.2014.0352 10.1103/PhysRevE.85.056314 10.1177/1748302620966705 10.1007/s00791-018-0289-y 10.1615/IntJMultCompEng.2011002402 10.1137/14096308X 10.1016/j.cam.2019.04.001 10.1002/cpe.4216
ContentType	Journal Article
Copyright	2021 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.
Copyright_xml	– notice: 2021 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.
DBID	AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U DOA
DOI	10.3390/math9121344
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection (subscription) ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central Engineering Research Database ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database (subscription) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering collection ProQuest Central Basic DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni)
DatabaseTitleList	Publicly Available Content Database CrossRef
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	2227-7390
ExternalDocumentID	oai_doaj_org_article_af7d4e68af0642c5b7c645efe200c158 10_3390_math9121344
GroupedDBID	-~X 5VS 85S 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABPPZ ABUWG ACIPV ACIWK ADBBV AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO GNUQQ GROUPED_DOAJ HCIFZ IAO K6V K7- KQ8 L6V M7S MODMG M~E OK1 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS RNS 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI PRINS Q9U
ID	FETCH-LOGICAL-c364t-134972cbf8d7ff34e33a1bc018abca71d4f4b34ad91fa6cda2f4b13b2aa787333
IEDL.DBID	BENPR
ISICitedReferencesCount	6
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000667913500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2227-7390
IngestDate	Fri Oct 03 12:39:51 EDT 2025 Fri Jul 25 12:07:11 EDT 2025 Sat Nov 29 07:15:43 EST 2025 Tue Nov 18 21:55:15 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	12
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c364t-134972cbf8d7ff34e33a1bc018abca71d4f4b34ad91fa6cda2f4b13b2aa787333
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
OpenAccessLink	https://www.proquest.com/docview/2545005167?pq-origsite=%requestingapplication%
PQID	2545005167
PQPubID	2032364
ParticipantIDs	doaj_primary_oai_doaj_org_article_af7d4e68af0642c5b7c645efe200c158 proquest_journals_2545005167 crossref_citationtrail_10_3390_math9121344 crossref_primary_10_3390_math9121344
PublicationCentury	2000
PublicationDate	2021-06-01
PublicationDateYYYYMMDD	2021-06-01
PublicationDate_xml	– month: 06 year: 2021 text: 2021-06-01 day: 01
PublicationDecade	2020
PublicationPlace	Basel
PublicationPlace_xml	– name: Basel
PublicationTitle	Mathematics (Basel)
PublicationYear	2021
Publisher	MDPI AG
Publisher_xml	– name: MDPI AG
References	Vabishchevich (ref_26) 2020; 80 Kay (ref_14) 2014; 11 (ref_5) 2018; 172 Yang (ref_35) 2014; 38 (ref_6) 2018; 114 Nakatsukasa (ref_21) 2018; 40 Zhang (ref_29) 2020; 405 Wu (ref_8) 2012; 13 Li (ref_36) 2020; 14 Lee (ref_17) 2018; 333 Ilic (ref_43) 2006; 9 Gao (ref_45) 2004; 303 Metzler (ref_12) 2004; 37 Vabishchevich (ref_27) 2020; 372 ref_16 Banjai (ref_24) 2019; 19 Balankin (ref_4) 2021; 85 Bonito (ref_19) 2015; 84 Margenov (ref_39) 2019; 31 Vabishchevich (ref_25) 2015; 282 Harizanov (ref_20) 2018; 25 Yang (ref_34) 2011; 33 Vabishchevich (ref_37) 2021; 165 Bonito (ref_23) 2018; 19 Tadjeran (ref_28) 2006; 213 Nochetto (ref_42) 2016; 54 (ref_7) 2009; 42 Yuste (ref_41) 2006; 216 Baeumer (ref_11) 2001; 37 Hofreither (ref_18) 2020; 80 ref_1 Alzahrani (ref_31) 2019; 361 Banjai (ref_32) 2019; 143 Baronas (ref_44) 2018; 23 ref_3 ref_2 Nochetto (ref_22) 2015; 15 Jumarie (ref_9) 2009; 22 Sabatelli (ref_13) 2002; 27 Saxton (ref_10) 2001; 81 Kay (ref_30) 2014; 54 Margenov (ref_38) 2017; 29 Melenk (ref_33) 2021; 41 Harizanov (ref_15) 2017; 310 Burch (ref_40) 2011; 9
References_xml	– volume: 27 start-page: 273 year: 2002 ident: ref_13 article-title: Waiting time distributions in financial markets publication-title: Eur. Phys. J. B doi: 10.1140/epjb/e20020151 – volume: 33 start-page: 1159 year: 2011 ident: ref_34 article-title: Novel numerical methods for solving the time-space fractional diffusion equations in two dimensions publication-title: SIAM J. Sci. Comput. doi: 10.1137/100800634 – volume: 333 start-page: 395 year: 2018 ident: ref_17 article-title: A second-order operator splitting Fourier spectral method for fractional-in-space reaction–diffusion equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2017.09.007 – volume: 405 start-page: 109141 year: 2020 ident: ref_29 article-title: A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2019.109141 – volume: 31 start-page: e5163 year: 2019 ident: ref_39 article-title: Scalability analysis of different parallel solvers for 3D fractional power diffusion problems publication-title: Concurr. Comput. Pract. Exper. doi: 10.1002/cpe.5163 – volume: 303 start-page: 186 year: 2004 ident: ref_45 article-title: How enzymes work: Analysis by modern rate theory and computer simulations publication-title: Science doi: 10.1126/science.1088172 – volume: 19 start-page: 901 year: 2019 ident: ref_24 article-title: Tensor FEM for spectral fractional diffusion publication-title: Found. Comput. Math. doi: 10.1007/s10208-018-9402-3 – volume: 84 start-page: 2083 year: 2015 ident: ref_19 article-title: Numerical approximation of fractional powers of elliptic operators publication-title: Math. Comput. doi: 10.1090/S0025-5718-2015-02937-8 – ident: ref_16 doi: 10.1201/b19666 – volume: 372 start-page: 112627 year: 2020 ident: ref_27 article-title: High order numerical schemes for solving fractional powers of elliptic operators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.112627 – volume: 42 start-page: 2614 year: 2009 ident: ref_7 article-title: Fractional Dirac operators and deformed field theory on Clifford algebra publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2009.04.002 – volume: 143 start-page: 177 year: 2019 ident: ref_32 article-title: A PDE approach to fractional diffusion: A space–fractional wave equation publication-title: Numer. Math. doi: 10.1007/s00211-019-01055-5 – volume: 37 start-page: 1543 year: 2001 ident: ref_11 article-title: Subordinated advection-dispersion equation for contaminant transport publication-title: Water Resour. Res. doi: 10.1029/2000WR900409 – ident: ref_1 – volume: 9 start-page: 333 year: 2006 ident: ref_43 article-title: Numerical approximation of a fractional-in-space diffusion equation–II-with nonhomogeneous boundary conditions publication-title: Fract. Calc. Appl. Anal. – volume: 165 start-page: 414 year: 2021 ident: ref_37 article-title: Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2021.03.006 – volume: 81 start-page: 2226 year: 2001 ident: ref_10 article-title: Anomalous subdidiffusion in fluorescence photobleaching recovery: A Monte Carlo study publication-title: Biophys. J. doi: 10.1016/S0006-3495(01)75870-5 – volume: 37 start-page: R161 year: 2004 ident: ref_12 article-title: The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics publication-title: J. Phys. A Math. Gen. doi: 10.1088/0305-4470/37/31/R01 – volume: 310 start-page: 115 year: 2017 ident: ref_15 article-title: Volume constrained 2-phase segmentation method utilizing a linear system solver based on the best uniform polynomial approximation of x−1/2 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2016.06.020 – volume: 38 start-page: 3755 year: 2014 ident: ref_35 article-title: A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2014.02.005 – volume: 172 start-page: 1617 year: 2018 ident: ref_5 article-title: Path integral formulation of fractionally perturbed Lagrangian oscillators on fractal publication-title: J. Stat. Phys. doi: 10.1007/s10955-018-2116-8 – volume: 40 start-page: A1494 year: 2018 ident: ref_21 article-title: The AAA algorithm for rational approximation publication-title: SIAM J. Sci. Comput. doi: 10.1137/16M1106122 – volume: 23 start-page: 437 year: 2018 ident: ref_44 article-title: Modelling the enzyme catalysed substrate conversion in a microbioreactor acting in continuous flow mode publication-title: Nonlinear Anal. Model. Control doi: 10.15388/NA.2018.3.9 – volume: 114 start-page: 516 year: 2018 ident: ref_6 article-title: Fractional derivatives with no-index law property: Application to chaos and statistics publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2018.07.033 – volume: 282 start-page: 289 year: 2015 ident: ref_25 article-title: Numerically solving an equation for fractional powers of elliptic operators publication-title: J. Comput. – volume: 41 start-page: 412 year: 2021 ident: ref_33 article-title: hp-FEM for the fractional heat equation publication-title: Ima J. Numer. Anal. doi: 10.1093/imanum/drz054 – volume: 216 start-page: 264 year: 2006 ident: ref_41 article-title: Weighted average finite difference methods forfractional diffusion equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.12.006 – volume: 54 start-page: 937 year: 2014 ident: ref_30 article-title: Fourier spectral methods for fractional-in-space reaction-diffusion equations publication-title: Bit Numer. Math. doi: 10.1007/s10543-014-0484-2 – volume: 213 start-page: 205 year: 2006 ident: ref_28 article-title: A second-order accurate numerical approximation for the fractional diffusion equation publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.08.008 – ident: ref_2 – ident: ref_3 doi: 10.1007/978-3-642-14003-7 – volume: 80 start-page: 332 year: 2020 ident: ref_18 article-title: A unified view of some numerical methods for fractional diffusion publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2019.07.025 – volume: 13 start-page: 45 year: 2012 ident: ref_8 article-title: Fractional Complexified Field Theory from Saxena-Kumbhat Fractional Integral, Fractional Derivative of Order (α,β) and Dynamical Fractional Integral Exponent publication-title: Afr. Diaspora J. Math. New Ser. – volume: 80 start-page: 305 year: 2020 ident: ref_26 article-title: Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2019.08.012 – volume: 22 start-page: 378 year: 2009 ident: ref_9 article-title: Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2008.06.003 – volume: 25 start-page: e2167 year: 2018 ident: ref_20 article-title: Optimal solvers for linear systems with fractional powers of sparse SPD matrices publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.2167 – volume: 15 start-page: 733 year: 2015 ident: ref_22 article-title: A PDE approach to fractional diffusion in general domains: A priori error analysis publication-title: Found. Comput. Math. doi: 10.1007/s10208-014-9208-x – volume: 11 start-page: 20140352 year: 2014 ident: ref_14 article-title: Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization publication-title: J. R. Soc. Interface doi: 10.1098/rsif.2014.0352 – volume: 85 start-page: 056314 year: 2021 ident: ref_4 article-title: Map of fluid flow in fractal porous medium into fractal continuum flow publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.85.056314 – volume: 14 start-page: 1 year: 2020 ident: ref_36 article-title: Splitting spectral element method for fractional reaction-diffusion equations publication-title: J. Algorithms Comput. Technol. doi: 10.1177/1748302620966705 – volume: 19 start-page: 19 year: 2018 ident: ref_23 article-title: Numerical methods for fractional diffusion publication-title: Comput. Vis. Sci. doi: 10.1007/s00791-018-0289-y – volume: 9 start-page: 661 year: 2011 ident: ref_40 article-title: Classical, nonlocal and fractional diffusion equations on bounded domains publication-title: Int. J. Multiscale Com. doi: 10.1615/IntJMultCompEng.2011002402 – volume: 54 start-page: 848 year: 2016 ident: ref_42 article-title: A PDE approach to space-time fractional parabolic problems publication-title: Siam J. Numer. Anal. doi: 10.1137/14096308X – volume: 361 start-page: 157 year: 2019 ident: ref_31 article-title: Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction–diffusion equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.04.001 – volume: 29 start-page: e4216 year: 2017 ident: ref_38 article-title: Parallel solvers for fractional power diffusion problems publication-title: Concurr. Comput. Pract. Exp. doi: 10.1002/cpe.4216
SSID	ssj0000913849
Score	2.1883447
Snippet	The main aim of this article is to analyze the efficiency of general solvers for parabolic problems with fractional power elliptic operators. Such discrete...
SourceID	doaj proquest crossref
SourceType	Open Website Aggregation Database Enrichment Source Index Database
StartPage	1344
SubjectTerms	Algorithms Approximation Boundary conditions Calculus discrete schemes Dynamical systems Food science fractional power elliptic operators Investigations Methods nonlinear diffusion-reaction Operators parabolic equations Splitting splitting methods stability
SummonAdditionalLinks	– databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA4iHvQgPrG-yMGTsNhs3kdfxYPWggrelmweWKht2a3-fifZbakoePG4y8AuM5PJzCTzfQidBaFE0ExmTogydqtUZpRTmWCaBWWEITwNCt_Lfl-9vurBEtVXvBPWwAM3irswQTrmhTIhpsqWl9IKxn3wYF5LeBrz7Uq9VEylGKwJVUw3A3kU6voLyP_edMIvY9-2oITU_yMQp92lt4U227QQXza_s41W_HgHbTwsMFXrXfR5ia8XpIF4EvDNEJY85Lz4CRT_7msM-SfufzRHMCM8b3hF0YGpwNijocWDhkCmxrEBi3tVM9cA4oNIl4bjFQ4IIhY_Tn06gK_30Evv9vn6LmtZEzJLBYvc8kzL3JZBORkCZZ5SQ0rbJcqU1kjiWGAlZcZpEoywzuTwTGiZGwOLl1K6j1bHk7E_QFhr3vWOa8U1Yya3ikPZSnIwiZDeBd1B53NFFraFFI_MFqMCSouo9WJJ6x10thCeNkgav4tdRYssRCL8dXoBTlG0TlH85RQddDy3Z9GuybqAUpjHGCTk4X984wit5_F-S-rIHKPVWfXhT9Ca_ZwN6-o0ueMXHAbnYg priority: 102 providerName: Directory of Open Access Journals
Title	A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators
URI	https://www.proquest.com/docview/2545005167 https://doaj.org/article/af7d4e68af0642c5b7c645efe200c158
Volume	9
WOSCitedRecordID	wos000667913500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: K7- dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database (subscription) customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: M7S dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: BENPR dateStart: 20130301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: PIMPY dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELag5QAHylMslJUPPSFFbeL3CbVlVyDoElGQyily_KArbXeXpO2R386Mkw1FIC5cLCWeg6UZj2c-j-cjZC9KLaPhKvNS1ohW6cxqrzPJDY_aSpuL9FD4g5rN9NmZKXvAre3LKjc-MTlqv3KIke9DIiPQgqR6vf6eIWsU3q72FBq3yTZ2KgM73z6azMpPA8qCXS81N93DPAb5_T7Egecm9THjvx1FqWP_Hw45nTLTnf9d3wNyv48v6WFnEA_JrbB8RO6dDM1Z28fk-pAeD-yDdBXpmzn4Dgie6Slo8CK0FAJZOrvq7nIWdIOcoWhpG7CaxdzRsmOiaSkiuXTadA8kQLxE3jWKtSDgjRz9uA7pJr99Qr5MJ5-P32Y9_ULmmORIUs-NKlwdtVcxMh4Ys3ntDnJta2dV7nnkNePWmzxa6bwt4DtndWEteAHG2FOytVwtwzNCjREHwQujheHcFk4LyH_zwkYlVfDRjMirjSYq1_cmR4qMRQU5CqqtuqG2EdkbhNddS46_ix2hSgcR7KOdfqyab1W_LStYgedBahsxEXOiVk5yEWIA5-FyoUdkd6Ptqt_cbfVL1c__Pf2C3C2wBCaBNrtk67K5Ci_JHXd9OW-bcW-r4wQDwPheZWMsPT3F8ccE5st3J-XXnz5r-9Q
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEB5VKRJw4I0IFNhDuSBZje31eveAUGmJGjUJlihSOZn1PiBSSILdFvGn-I3M-AUIxK0HjrbnYHu__XZndmY-gF0vpPCKp4EVoqBolQy0tDIQXHEvtdBhUhcKT9P5XJ6eqmwLvne1MJRW2XFiTdR2bShGvoeOTEIIEunLzZeAVKPodLWT0Ghgcey-fUWXrXoxOcTxfRZF49cnB0dBqyoQmFhw0l7nKo1M4aVNvY-5i2MdFmYUSl0YnYaWe17EXFsVei2M1RFeh3ERaY3gjikAipS_zRHsowFsZ5NZ9r6P6lCXTclVUwgYx2q0h_vOT6rum8Z_W_pqhYA_FoB6VRvf_N_-xy240e6f2X4D-Nuw5VZ34Pqsbz5b3YWLfXbQqyuytWeHC-RGdA7YW0ToZ1cx3Kiz-XlzVrVkXWSQTDNd4qxYLgzLGqWdilGkmo3LpgAEzTPSlWOU64Jsa9ibjaszFap78O5SPvw-DFbrlXsATKlk5GyiZKI415GRCfr3YaR9KlJnvRrC827kc9P2XicJkGWOPhjBJP8FJkPY7Y03TcuRv5u9Igj1JtQnvL6xLj_mLe3k-AaWOyG1J0fTJEVqBE-cd0iOJkzkEHY6dOUteVX5T2g9_Pfjp3D16GQ2zaeT-fEjuBZRuk8doNqBwVl57h7DFXNxtqjKJ-08YfDhsqH4A5fgVYc
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwELaqLUJw4F2xUMCHckGKdhM7fhxQ1Xa7ompZIh5Sb8HxA1ZadpekLeKv9dcxkxcgELceOCaZQxJ__uwZz8xHyE4QSgTNZeSEKDBapSKjnIoE1zwoI0yc1oXCJ3I2U6enOtsgl10tDKZVdpxYE7VbWYyRj8CRSRFBQo5CmxaRTaa7668RKkjhSWsnp9FA5Nh__wbuW_XyaAJj_TxJpofvD15FrcJAZJngqMPOtUxsEZSTITDuGTNxYcexMoU1MnY88IJx43QcjLDOJHAdsyIxBoDOMBgK9L8pGTg9A7K5fzjL3vYRHuy4qbhuigIZ0-MR7EE_67qHGv9tGazVAv5YDOoVbnr7f_43d8itdl9N95qJcJds-OU9cvN135S2uk8u9uhBr7pIV4FO5sCZ4DTQd4DcL76isIGns_PmDGtBu4ghmmamhNmymFuaNQo8FcUINp2WTWEImGeoN0cxBwZY2NI3a19nMFQPyIcr-fAtMliulv4hoVqnY-9SrVLNuUmsSsHvjxMTpJDeBT0kLzoU5LbtyY7SIIscfDOETP4LZIZkpzdeN61I_m62j3DqTbB_eH1jVX7KWzrK4Q0c90KZgA6oTQtpBU998ECaNk7VkGx3SMtbUqvynzB79O_Hz8h1wF9-cjQ7fkxuJJgFVMettsngrDz3T8g1e3E2r8qn7ZSh5ONVI_EHNXdeIQ
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Comparison+of+Discrete+Schemes+for+Numerical+Solution+of+Parabolic+Problems+with+Fractional+Power+Elliptic+Operators&rft.jtitle=Mathematics+%28Basel%29&rft.au=%C4%8Ciegis%2C+Raimondas&rft.au=%C4%8Ciegis%2C+Remigijus&rft.au=Dap%C5%A1ys%2C+Ignas&rft.date=2021-06-01&rft.issn=2227-7390&rft.eissn=2227-7390&rft.volume=9&rft.issue=12&rft.spage=1344&rft_id=info:doi/10.3390%2Fmath9121344&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_math9121344
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2227-7390&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2227-7390&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2227-7390&client=summon