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Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-06-01
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities.
The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space W230,1, whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values.
An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach.
The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform.
Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments.
Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
American Psychological Association (APA)
Abu Arqub, Omar. 2015. Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074031
Modern Language Association (MLA)
Abu Arqub, Omar. Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems. Mathematical Problems in Engineering No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1074031
American Medical Association (AMA)
Abu Arqub, Omar. Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074031
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074031