@Article{JCM-40-2,
author = {Liu, Libin and Yanping, Chen and Ying, Liang},
title = {Numerical Analysis of a Nonlinear Singularly Perturbed Delay Volterra Integro-Differential Equation on an Adaptive Grid},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {2},
pages = {258--274},
abstract = {<p style="text-align: justify;">In this paper, we study a nonlinear first-order singularly perturbed Volterra integro-differential equation with delay. This equation is discretized by the backward Euler for
differential part and the composite numerical quadrature formula for integral part for which
both an a priori and an a posteriori error analysis in the maximum norm are derived. Based
on the a priori error bound and mesh equidistribution principle, we prove that there exists
a mesh gives optimal first order convergence which is robust with respect to the perturbation parameter. The a posteriori error bound is used to choose a suitable monitor function
and design a corresponding adaptive grid generation algorithm. Furthermore, we extend
our presented adaptive grid algorithm to a class of second-order nonlinear singularly perturbed delay differential equations. Numerical results are provided to demonstrate the
effectiveness of our presented monitor function. Meanwhile, it is shown that the standard arc-length monitor function is unsuitable for this type of singularly perturbed delay
differential equations with a turning point.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2008-m2020-0063},
url = {https://global-sci.com/article/84177/numerical-analysis-of-a-nonlinear-singularly-perturbed-delay-volterra-integro-differential-equation-on-an-adaptive-grid}
}