| Autor: |
Richard Avery, Douglas R. Anderson, Jeffrey Lyons |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Axioms, Vol 13, Iss 4, p 222 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms13040222 |
| Popis: |
Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green’s function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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