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
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.