@article{Cen2022, 
author = {Zhongdi Cen and Jian Huang and Aimin Xu},
title = {A posteriori mesh method for a system of singularly perturbed initial value problems},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16719-16732},
keywords = {singular perturbation, hybrid difference scheme, mesh equidistribution, a posteriori error analysis, second order problems},
url = {https://www.sciopen.com/article/10.3934/math.2022917},
doi = {10.3934/math.2022917},
abstract = {A system of singularly perturbed initial value problems with weak constrained conditions on the coefficients is considered. First the system of second-order singularly perturbed problems is transformed into a system of first-order singularly perturbed problems with integral terms, which facilitates the subsequent stability and a posteriori error analyses. Then a hybrid difference method with the use of interpolating quadrature rules is utilized to approximate the transformed system. Next a posteriori error analysis for the discretization scheme on an arbitrary mesh is presented. A solution-adaptive algorithm based on a posteriori error estimation is devised to generate a posteriori mesh and obtain approximation solution. Finally numerical experiments show a uniform convergence behavior of second-order for the scheme, which improves the previous results and achieves the optimal convergence order under the given discrete scheme.}
}