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Article: Fast and High-Order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in R2

TitleFast and High-Order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in R2
Authors
KeywordsTwo-dimensional time-dependent nonlocal problems
Nonsymmetric indefinite systems
Rectangular matrices
Conjugate gradient squares method
Stability and convergence analysis
Issue Date2020
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474
Citation
Journal of Scientific Computing, 2020, v. 84, p. article no. 8 How to Cite?
AbstractIn this paper, we study the Crank–Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such discretization are that the proposed numerical method is unconditionally stable and its global truncation error is of O(τ2+h4−γ) with 0<γ<1, where τ and h are the discretization sizes in the temporal and spatial dimensions respectively. Also we develop the conjugate gradient squared method to solving the resulting discretized nonsymmetric and indefinite systems arising from time-dependent nonlocal problems including two-dimensional cases. By using additive and multiplicative Cauchy kernels in nonlocal problems, structured coefficient matrix-vector multiplication can be performed efficiently in the conjugate gradient squared iteration. Numerical examples are given to illustrate our theoretical results and demonstrate that the computational cost of the proposed method is of O(MlogM) operations where M is the number of collocation points.
Persistent Identifierhttp://hdl.handle.net/10722/287671
ISSN
2019 Impact Factor: 2.228
2015 SCImago Journal Rankings: 1.724
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCao, R-
dc.contributor.authorChen, M-
dc.contributor.authorNg, MK-
dc.contributor.authorWu, YJ-
dc.date.accessioned2020-10-05T12:01:31Z-
dc.date.available2020-10-05T12:01:31Z-
dc.date.issued2020-
dc.identifier.citationJournal of Scientific Computing, 2020, v. 84, p. article no. 8-
dc.identifier.issn0885-7474-
dc.identifier.urihttp://hdl.handle.net/10722/287671-
dc.description.abstractIn this paper, we study the Crank–Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such discretization are that the proposed numerical method is unconditionally stable and its global truncation error is of O(τ2+h4−γ) with 0<γ<1, where τ and h are the discretization sizes in the temporal and spatial dimensions respectively. Also we develop the conjugate gradient squared method to solving the resulting discretized nonsymmetric and indefinite systems arising from time-dependent nonlocal problems including two-dimensional cases. By using additive and multiplicative Cauchy kernels in nonlocal problems, structured coefficient matrix-vector multiplication can be performed efficiently in the conjugate gradient squared iteration. Numerical examples are given to illustrate our theoretical results and demonstrate that the computational cost of the proposed method is of O(MlogM) operations where M is the number of collocation points.-
dc.languageeng-
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474-
dc.relation.ispartofJournal of Scientific Computing-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI]-
dc.subjectTwo-dimensional time-dependent nonlocal problems-
dc.subjectNonsymmetric indefinite systems-
dc.subjectRectangular matrices-
dc.subjectConjugate gradient squares method-
dc.subjectStability and convergence analysis-
dc.titleFast and High-Order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in R2-
dc.typeArticle-
dc.identifier.emailNg, MK: michael.ng@hku.hk-
dc.identifier.authorityNg, MK=rp02578-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10915-020-01260-7-
dc.identifier.scopuseid_2-s2.0-85086761993-
dc.identifier.hkuros315732-
dc.identifier.volume84-
dc.identifier.spagearticle no. 8-
dc.identifier.epagearticle no. 8-
dc.identifier.isiWOS:000544921000001-
dc.publisher.placeUnited States-
dc.identifier.issnl0885-7474-

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