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A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-09
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
A new collocation method is developed for solving BVPs which arise from the problems in calculus of variation.
These BVPs result from the Euler-Lagrange equations, which are the necessary conditions of the extremums of problems in calculus of variation.
The proposed method is based upon the Bernoulli polynomials approximation together with their operational matrix of differentiation.
After imposing the collocation nodes to the main BVPs, we reduce the variational problems to the solution of algebraic equations.
It should be noted that the robustness of operational matrices of differentiation with respect to the integration ones is shown through illustrative examples.
Complete comparisons with other methods and superior results confirm the validity and applicability of the presented method.
American Psychological Association (APA)
Tohidi, Emran& Kiliçman, Adem. 2013. A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1010639
Modern Language Association (MLA)
Tohidi, Emran& Kiliçman, Adem. A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation. Mathematical Problems in Engineering No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-1010639
American Medical Association (AMA)
Tohidi, Emran& Kiliçman, Adem. A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1010639
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1010639