Solving a nonlinear biharmonic boundary value problem
Author affiliations
DOI:
https://doi.org/10.15625/1813-9663/33/4/11066Keywords:
Nonlinear biharmonic boundary value problem, Existence and uniqueness of solution, Iterative method, Numerical solutionAbstract
In this paper we study a boundary value problem for a nonlinear biharmonic equation, which models a bending plate on nonlinear elastic foundation. We propose a new approach to existence and uniqueness and numerical solution of the problem. It is based on the reduction of the problem to finding fixed point of a nonlinear operator for the nonlinear term. The result is that under some easily verified conditions we have established the existence and uniqueness of a solution and the convergence of an iterative method for the solution. The positivity of the solution and the monotony of iterations are also considered. Some examples demonstrate the applicability of the obtained theoretical results and the efficiency of the iterative method.Metrics
Metrics Loading ...
Downloads
Published
11-05-2018
How to Cite
[1]
D. Q. A, T. H. Hai, N. T. Huong, and N. T. K. Quy, “Solving a nonlinear biharmonic boundary value problem”, JCC, vol. 33, no. 4, p. 308–324, May 2018.
Issue
Section
Articles
License
1. We hereby assign copyright of our article (the Work) in all forms of media, whether now known or hereafter developed, to the Journal of Computer Science and Cybernetics. We understand that the Journal of Computer Science and Cybernetics will act on my/our behalf to publish, reproduce, distribute and transmit the Work.2. This assignment of copyright to the Journal of Computer Science and Cybernetics is done so on the understanding that permission from the Journal of Computer Science and Cybernetics is not required for me/us to reproduce, republish or distribute copies of the Work in whole or in part. We will ensure that all such copies carry a notice of copyright ownership and reference to the original journal publication.
3. We warrant that the Work is our results and has not been published before in its current or a substantially similar form and is not under consideration for another publication, does not contain any unlawful statements and does not infringe any existing copyright.
4. We also warrant that We have obtained the necessary permission from the copyright holder/s to reproduce in the article any materials including tables, diagrams or photographs not owned by me/us.
