2 research outputs found
A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference method (FOFDM) to solve the resulting set of linear problems (one at each time level). We prove that the underlying fitted operator satisfies the maximum principle. This result is then used in the error analysis of the FOFDM. The method is shown to be first order convergent in time and second order convergent in space, uniformly with respect to the perturbation parameter. We test the method on several numerical examples to confirm our theoretical findings.Web of Scienc
A new parameter-uniform discretization of semilinear singularly perturbed problems
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