A posteriori error estimation for quasilinear singularly perturbed problems with integral boundary condition

Abstract

We consider a quasilinear singularly perturbed parametrized problem with integral boundary condition. To solve the problem numerically, the discretization comprises of an implicit Euler scheme for the quasilinear problem and a composite right rectangle rule for the integral boundary condition. We establish a posteriori error estimate for the discrete problem that holds true uniformly in the small perturbation parameter. Further, we rectify the shortcomings of a posteriori error estimation in L.-B. Liu et al. (Numerical Algorithms 83:719–739, 2019) for a different class of problems. Numerical experiments are performed and results are reported for validation of the theoretical error estimates. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.