Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems

The paper is concerned with Strongly nonlinear singularly perturbed boundary value problems in one dimension. The problems are solved numerically by finite-difference schemes on special meshes which are dense in the boundary layers. The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed. For the central scheme, error estimates are derived in a discrete L-1 norm. They are of second order and decrease together with the perturbation parameter epsilon. The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically Numerical results show epsilon-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.