New parameter-uniform discretisations of singularly perturbed Volterra integro-differential equations

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dc.contributor.authorIragi, Bakulikira C.
dc.contributor.authorMunyakazi, Justin B.
dc.date.accessioned2019-10-18T10:30:20Z
dc.date.available2019-10-18T10:30:20Z
dc.date.issued2018
dc.description.abstractWe design and analyse two numerical methods namely a fitted mesh and a fitted operator finite difference methods for solving singularly perturbed Volterra integro-differential equations. The fitted mesh method we propose is constructed using a finite difference operator to approximate the derivative part and some suitably chosen quadrature rules for the integral part. To obtain a parameter-uniform convergence, we use a piecewise-uniform mesh of Shishkin type. On the other hand, to construct the fitted operator method, the Volterra integro-differential equation is discretised by introducing a fitting factor via the method of integral identity with the use of exponential basis function along with interpolating quadrature rules [2]. The two methods are analysed for convergence and stability. We show that the two methods are robust with respect to the perturbation parameter. Two numerical examples are solved to show the applicability of the proposed schemes.en_US
dc.identifier.citationIragi, Bakulikira C. & Munyakazi, Justin B. (2018). New parameter-uniform discretisations of singularly perturbed Volterra integro-differential equations. Applied Mathematics & Information Sciences, 12(3), 517-527. http://dx.doi.org/10.18576/amis/120306en_US
dc.identifier.issn2325-0399
dc.identifier.urihttp://dx.doi.org/10.18576/amis/120306
dc.identifier.urihttp://hdl.handle.net/10566/5046
dc.language.isoenen_US
dc.publisherNatural Sciences Publishingen_US
dc.subjectSingularly perturbed problemsen_US
dc.subjectVolterra integro-differential equationsen_US
dc.subjectBoundary layeren_US
dc.subjectFinite difference schemesen_US
dc.subjectUniform convergenceen_US
dc.titleNew parameter-uniform discretisations of singularly perturbed Volterra integro-differential equationsen_US
dc.typeArticleen_US

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