Report Number: CS-TR-75-530
Institution: Stanford University, Department of Computer Science
Title: An adaptive finite difference solver for nonlinear two point boundary problems with mild boundary layers.
Author: Lentini, M.
Author: Pereyra, Victor
Date: November 1975
Abstract: A variable order variable step finite difference algorithm for approximately solving m-dimensional systems of the form y' = f(t,y), t $\in$ [a,b] subject to the nonlinear boundary conditions g(y(a),y(b)) = 0 is presented. A program, PASVAR, implementing these ideas has been written and the results on several test runs are presented together with comparisons with other methods. The main features of the new procedure are: a) Its ability to produce very precise global error estimates, which in turn allow a very fine control between desired tolerance and actual output precision. b) Non-uniform meshes allow an economical and accurate treatment of boundary layers and other sharp changes in the solutions. c) The combination of automatic variable order (via deferred corrections) and automatic (adaptive) mesh selection produces, as in the case of initial value problem solvers, a versatile, robust, and efficient algorithm.