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Richardson Extrapolation Method on an Adaptive Grid for Singularly Perturbed Volterra Integro-Differential Equations
Ist Teil von
Numerical functional analysis and optimization, 2021-07, Vol.42 (7), p.739-757
Ort / Verlag
Abingdon: Taylor & Francis
Erscheinungsjahr
2021
Link zum Volltext
Quelle
Taylor & Francis Journals Auto-Holdings Collection
Beschreibungen/Notizen
In this paper, an adaptive grid method for singularly perturbed Volterra integro-differential equations exhibiting a boundary layer is studied. At first, based on an arbitrary nonuniform mesh, we use the classical backward Euler formula to discrete the first-order derivative part and the left rectangle formula to approximate the integral part, respectively. Meanwhile, it is shown from the mesh equidistribution principle and the truncation error analysis that the presented adaptive grid method is first-order uniformly convergent with respect to the perturbation parameter. Furthermore, the Richardson extrapolation technique is utilized to improve the uniform accuracy of the presented adaptive grid method in the discrete supremum norm form
to
where
is the mesh parameter. Finally, some numerical results are given to support the theoretical results.