Samir Karasulji´ckarasulji´c’s scientific contributions

In this paper we consider the numerical solution of a singularly perturbed one-dimensional semilinear reaction-diffusion problem. We construct a class of finite-difference schemes to discretize the problem and we prove that the discrete system has a unique solution. The central result of the paper is second-order convergence uniform in the perturbation parameter, which we obtain for the discrete approximate solution on a modified Bakhvalov mesh. Numerical experiments with two representatives of the class of difference schemes show that our method is robust and confirm the theoretical results.