@article{Mao2023, 
author = {Zhi Mao and Dan Luo},
title = {A robust adaptive grid method for first-order nonlinear singularly perturbed Fredholm integro-differential equations},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {3},
pages = {1006-1023},
keywords = {Fredholm integro-differential equation, singularly perturbed problem, adaptive grid algorithm, ε-uniform convergence},
url = {https://www.sciopen.com/article/10.3934/nhm.2023044},
doi = {10.3934/nhm.2023044},
abstract = {In this paper, a robust adaptive grid method is developed for solving first-order nonlinear singularly perturbed Fredholm integro-differential equations (SPFIDEs). Firstly such SPFIDEs are discretized by the backward Euler formula for differential part and the composite numerical quadrature rule for integral part. Then both a prior and an a posterior error analysis in the maximum norm are derived. Based on the prior error bound and the mesh equidistribution principle, it is proved that there exists a mesh gives optimal first-order convergence which is robust with respect to the perturbation parameter. Finally, the posterior error bound is used to choose a suitable monitor function and design a corresponding adaptive grid generation algorithm. Numerical results are given to illustrate our theoretical result.}
}