International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 499-505
Rapid convergence of approximate solutions for first order nonlinear boundary value problems
1Departamento de Anàlise Matemhtica, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15706, Spain
2Department of Mathematical Sciences, University of Oulu, Oulu 57 90570, Finland
Received 20 August 1996
Copyright © 1998 Alberto Cabada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we study the convergence of the approximate solutions for the following
first order problem
Here is such that
exists and is a continuous function for some . Under some
additional conditions on , we prove that it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order .