High-order convergent methods for singularly perturbed quasilinear problems with integral boundary conditions

Abstract

In this work, we develop a numerical scheme for a class of singularly perturbed quasilinear problems with integral boundary conditions. The quasilinear equation is discretized using a hybrid scheme, and the composite trapezoidal rule is used to discretize the boundary condition. We construct a general error analysis framework for the discrete scheme. Within this framework, the discrete scheme is shown to be uniformly convergent of (Formula presented.) on Shishkin meshes and (Formula presented.) on Bakhvalov meshes. Further, we propose adaptive generation of meshes based on a suitable monitor function and the mesh equidistribution principle. We prove that on these meshes the discrete scheme is uniformly convergent of (Formula presented.) Our theoretical findings are supported by numerical results obtained through experiments. © 2020 John Wiley & Sons, Ltd.