An accelerated monotone iterative method for a boundary value problem of secondorder discrete equations is presented. This method leads to an existence-comparieon theorem as well as a computational algorithm for the solutions. The monotone property of the iterations gives improved upper and lower bo
Monotone methods for a discrete boundary problem
โ Scribed by Wan Zhuang; Yubo Chen; Sui Sun Cheng
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 422 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0898-1221
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โฆ Synopsis
This paper is motivated by recent interests in space discrete Nagumo equations and is concerned with the existence of solutions of a nonlinear discrete boundary value problem. Monotone methods are used to derive the existence theorems. These methods, as is well known, provide constructive schemes for calculating the solutions.
๐ SIMILAR VOLUMES
A new concept of a pair of upper and lower solutions is introduced for a class of discrete boundary value problems without monotone nonlinearities. Some comparison results are established. An existence and enclosing theorem for the solutions is given in terms of upper and lower solutions. A new mono