A combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg-de Vries (KdV) equation

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dc.authorid0000-0003-1846-0817en_US
dc.authorid0000-0002-6655-3543en_US
dc.contributor.authorPolat, Murat
dc.contributor.authorOruç, Ömer
dc.date.accessioned2021-11-11T10:57:07Z
dc.date.available2021-11-11T10:57:07Z
dc.date.issued2021en_US
dc.departmentDicle Üniversitesi, Fen Fakültesi, Matematik Bölümüen_US
dc.descriptionWOS:000711159100003
dc.description.abstractIn this work, we develop a novel method to obtain numerical solution of well-known Korteweg-de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to combine DBFs and high order geometric numerical integrator for solving such a nonlinear partial differential equation (PDE) which preserves conservation laws. To demonstrate the performance of the proposed method we consider five test problems. We reckon L-infinity, L-2 and root mean square (RMS) errors and compare them with other results available in the literature. Besides the errors, we also monitor conservation laws of the KDV equation and we show that the method in this paper produces accurate results and preserves the conservation laws quite good. Numerical outcomes show that the present novel method is efficient and reliable for PDEs.en_US
dc.identifier.citationPolat, M. ve Oruç, Ö. (2021). A combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg-de Vries (KdV) equation. International Journal of Geometric Methods in Modern Physics, 18(13).en_US
dc.identifier.doi10.1142/S0219887821502169
dc.identifier.issn0219-8878
dc.identifier.issn1793-6977
dc.identifier.issue13en_US
dc.identifier.scopus2-s2.0-85116888454
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://hdl.handle.net/11468/8229
dc.identifier.volume18en_US
dc.identifier.wosWOS:000711159100003
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorPolat, Murat
dc.institutionauthorOruç, Ömer
dc.language.isoenen_US
dc.publisherWorld Scientific Publicationen_US
dc.relation.ispartofInternational Journal of Geometric Methods in Modern Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectDelta-shaped basis functionsen_US
dc.subjectGroup-preserving schemeen_US
dc.subjectgeometric integratoren_US
dc.subjectKdV equationen_US
dc.subjectNumerical solutionen_US
dc.titleA combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg-de Vries (KdV) equationen_US
dc.titleA combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg-de Vries (KdV) equation
dc.typeArticleen_US

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