Document Type
Article
Publication Date
10-2019
Publication Source
Georgian Mathematical Journal
Abstract
A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.
ISBN/ISSN
1572-9176
Document Version
Published Version
Publisher
De Gruyter
Volume
28
Issue
2
Peer Reviewed
yes
Keywords
Boundary value problem at resonance, shift method, upper and lower solutions, quasilinearization
eCommons Citation
Alanazi, Kareem; Alshammari, Meshal; and Eloe, Paul W., "Quasilinearization and Boundary Value Problems at Resonance" (2019). Mathematics Faculty Publications. 208.
https://ecommons.udayton.edu/mth_fac_pub/208
Comments
Document is made available for download with the permission of the author in compliance with the publisher's policy on self-archiving. Permission documentation is on file.