A high order convergent adaptive numerical method for singularly perturbed nonlinear systems

Abstract

In this work, we develop a high order convergent adaptive numerical method for a system of first-order singularly perturbed nonlinear differential equations with distinct perturbation parameters. The problem is discretized by a hybrid finite difference scheme for which a posteriori error estimate in the maximum norm is derived. The layer-adapted meshes are generated using equidistribution of the monitor function chosen based on the derived a posteriori error estimate. Numerical results are presented that validate the theory and show the effectiveness of the present numerical method. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.