An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers

A variable order finite difference solver for first order nonlinear systems subject to two-point boundary conditions is described. The method uses deferred corrections and adaptive meshes are automatically produced in order to detect and resolve mild boundary layers and other sharp gradient situations. A set of numerical examples solved with an implementation of the algorithm is presented, together with comparisons with several other codes.