Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations
- Resource Type
- Article
- Authors
- Henderson, Johnny; Thompson, H. B.
- Source
- The Journal of Difference Equations and Applications; January 2001, Vol. 7 Issue: 2 p297-321, 25p
- Subject
- Language
- ISSN
- 10236198; 15635120
We study the continuous problem[image omitted] and its discrete approximation[image omitted] where f and[image omitted] are continuous and fully nonlinear[image omitted] and[image omitted] We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to-the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.