Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions
Joint Authors
Anderson, Douglas Robert
Tisdell, Christopher C.
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-08-24
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We investigate two types of first-order, two-point boundary value problems (BVPs).
Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP).
We formulate some sufficient conditions under which the discrete BVP will admit solutions.
For this, our choice of methods involves a monotone iterative technique and the method of successive approximations (a.k.a.
Picard iterations) in the absence of Lipschitz conditions.
Our existence results for the discrete BVP are of a constructive nature and are of independent interest in their own right.
We then turn our attention to applying our existence results for the discrete BVP to the continuous BVP.
We form new existence results for solutions to the continuous BVP with our methods involving linear interpolation of the data from the discrete BVP, combined with a priori bounds and the convergence Arzela-Ascoli theorem.
Thus, our use of discrete BVPs to yield results for the continuous BVP may be considered as a discrete approach to continuous BVPs.
American Psychological Association (APA)
Anderson, Douglas Robert& Tisdell, Christopher C.. 2016. Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions. Abstract and Applied Analysis،Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1094745
Modern Language Association (MLA)
Anderson, Douglas Robert& Tisdell, Christopher C.. Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions. Abstract and Applied Analysis No. 2016 (2016), pp.1-6.
https://search.emarefa.net/detail/BIM-1094745
American Medical Association (AMA)
Anderson, Douglas Robert& Tisdell, Christopher C.. Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions. Abstract and Applied Analysis. 2016. Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1094745
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1094745