A new parameter-uniform discretization of semilinear singularly perturbed problems
Abstract
In this paper, we present a numerical approach to solving singularly perturbed semilinear
convection-diffusion problems. The nonlinear part of the problem is linearized via the quasilinearization
technique. We then design and implement a fitted operator finite difference method to solve the
sequence of linear singularly perturbed problems that emerges from the quasilinearization process.
We carry out a rigorous analysis to attest to the convergence of the proposed procedure and notice
that the method is first-order uniformly convergent. Some numerical evaluations are implemented on
model examples to confirm the proposed theoretical results and to show the efficiency of the method.