A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems

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dc.contributor.authorMunyakazi, Justin B.
dc.contributor.authorPatidar, Kailash C.
dc.date.accessioned2018-01-15T11:27:46Z
dc.date.available2018-01-15T11:27:46Z
dc.date.issued2013
dc.description.abstractThis paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference method (FOFDM) to solve the resulting set of linear problems (one at each time level). We prove that the underlying fitted operator satisfies the maximum principle. This result is then used in the error analysis of the FOFDM. The method is shown to be first order convergent in time and second order convergent in space, uniformly with respect to the perturbation parameter. We test the method on several numerical examples to confirm our theoretical findings.en_US
dc.description.accreditationWeb of Science
dc.identifier.citationMunyakazi, J.B. & Patidar, K.C. (2013). A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems. Computational and Applied Mathematics, 32: 509 – 519en_US
dc.identifier.issn0101-8205
dc.identifier.urihttp://dx.doi.org/10.1007/s40314-013-0033-7
dc.identifier.urihttp://hdl.handle.net/10566/3389
dc.language.isoenen_US
dc.privacy.showsubmitterFALSE
dc.publisherSpring Verlagen_US
dc.rightsThis is the author-version of the article published online at: http://dx.doi.org/10.1007/s40314-013-0033-7
dc.status.ispeerreviewedTRUE
dc.subjectParabolic reaction-diffusion problemsen_US
dc.subjectSingular perturbationsen_US
dc.subjectFitted operator finite difference methodsen_US
dc.subjectError boundsen_US
dc.subjectUniform convergenceen_US
dc.titleA fitted numerical method for singularly perturbed parabolic reaction-diffusion problemsen_US
dc.typeArticleen_US

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