Galerkin-Petrov method for strongly nonlinear singularly perturbed boundary value problems on special meshes (Q1375428)

The authors solve numerically a class of strongly nonlinear singularly perturbed boundary value problems by the Galerkin-Petrov method. Special adaptive meshes and parabolic splines are used for this purpose. A theorem concerning the convergence of the approximate solutions to the exact solution is established. Error estimates of order \(O(1/m^2)\) in the \(L_\infty\)-norm are obtained, where \(m\) is the number of knots of the special partition. A numerical example is given to illustrate the results.