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dc.contributor.authorErbay, Hüsnü Ata
dc.contributor.authorErbay, Saadet
dc.contributor.authorErkip, A.
dc.date.accessioned2019-03-29T12:40:58Z
dc.date.available2019-03-29T12:40:58Z
dc.date.issued2018-09-13
dc.identifier.issn0764-583Xen_US
dc.identifier.urihttp://hdl.handle.net/10679/6249
dc.identifier.urihttps://www.esaim-m2an.org/articles/m2an/abs/2018/03/m2an170176/m2an170176.html
dc.description.abstractIn this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important characteristic of the numerical method is that it is directly applied to the nonlocal equation by introducing the discrete convolution operator. Starting from the continuous Cauchy problem defined on the real line, we first construct the discrete Cauchy problem on a uniform grid of the real line. Thus the semi-discretization in space of the continuous problem gives rise to an infinite system of ordinary differential equations in time. We show that the initial-value problem for this system is well-posed. We prove that solutions of the discrete problem converge uniformly to those of the continuous one as the mesh size goes to zero and that they are second-order convergent in space. We then consider a truncation of the infinite domain to a finite one. We prove that the solution of the truncated problem approximates the solution of the continuous problem when the truncated domain is sufficiently large. Finally, we present some numerical experiments that confirm numerically both the expected convergence rate of the semi-discrete scheme and the ability of the method to capture finite-time blow-up of solutions for various convolution kernels.en_US
dc.language.isoengen_US
dc.publisherEDP Sciencesen_US
dc.relation.ispartofESAIM: Mathematical Modelling and Numerical Analysis
dc.rightsrestrictedAccess
dc.titleConvergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equationsen_US
dc.typeArticleen_US
dc.peerreviewedyesen_US
dc.publicationstatusPublisheden_US
dc.contributor.departmentÖzyeğin University
dc.contributor.authorID(ORCID 0000-0002-5167-609X & YÖK ID 119316) Erbay, Hüsnü Ata
dc.contributor.authorID(ORCID 0000-0002-6080-4591 & YÖK ID 119313) Erbay, Saadet
dc.contributor.ozuauthorErbay, Hüsnü Ata
dc.contributor.ozuauthorErbay, Saadet
dc.identifier.volume52en_US
dc.identifier.issue3en_US
dc.identifier.startpage803en_US
dc.identifier.endpage826en_US
dc.identifier.wosWOS:000444551600001
dc.identifier.doi10.1051/m2an/2018035en_US
dc.subject.keywordsNonlocal nonlinear wave equationen_US
dc.subject.keywordsDiscretizationen_US
dc.subject.keywordsSemi-discrete schemeen_US
dc.subject.keywordsImproved Boussinesq equationen_US
dc.subject.keywordsConvergenceen_US
dc.identifier.scopusSCOPUS:2-s2.0-85053563455
dc.contributor.authorMale1
dc.contributor.authorFemale1
dc.relation.publicationcategoryArticle - International Refereed Journal - Institution Academic Staff


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