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New Parameter-Uniform Discretisations of Singularly Perturbed Volterra Integro-Differential Equations |
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PP: 517-527 |
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doi:10.18576/amis/120306
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Author(s) |
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Bakulikira C. Iragi,
Justin B. Munyakazi,
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Abstract |
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| We 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. |
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