Report Number: CS-TR-73-348
Institution: Stanford University, Department of Computer Science
Title: High order finite difference solution of differential equations.
Author: Pereyra, Victor
Date: April 1973
Abstract: These seminar notes give a detailed treatment of finite difference approximations to smooth nonlinear two-point boundary value problems for second order differential equations. Consistency, stability, convergence, and asymptotic expansions are discussed. Most results are stated in such a way as to indicate extensions to more general problems. Successive extrapolations and deferred corrections are described and their implementations are explored thoroughly. A very general deferred correction generator is developed and it is employed in the implementation of a variable order, variable (uniform) step method. Complete FORTRAN programs and extensive numerical experiments and comparisons are included together with a set of 48 references.