A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation

A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation

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 Bernoull...

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Main Authors: Emran Tohidi, Adem Kılıçman
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/757206
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spelling doaj-d259fac07c954ee693a914aa8f62c39a2020-11-24T21:05:33ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/757206757206A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of VariationEmran Tohidi0Adem Kılıçman1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, IranDepartment of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaA 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.http://dx.doi.org/10.1155/2013/757206
collection DOAJ
language English
format Article
sources DOAJ
author Emran Tohidi
Adem Kılıçman
spellingShingle Emran Tohidi
Adem Kılıçman
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
author_facet Emran Tohidi
Adem Kılıçman
author_sort Emran Tohidi
title A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
title_short A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
title_full A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
title_fullStr A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
title_full_unstemmed A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation
title_sort collocation method based on the bernoulli operational matrix for solving nonlinear bvps which arise from the problems in calculus of variation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/757206
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AT ademkılıcman acollocationmethodbasedonthebernoullioperationalmatrixforsolvingnonlinearbvpswhicharisefromtheproblemsincalculusofvariation
AT emrantohidi collocationmethodbasedonthebernoullioperationalmatrixforsolvingnonlinearbvpswhicharisefromtheproblemsincalculusofvariation
AT ademkılıcman collocationmethodbasedonthebernoullioperationalmatrixforsolvingnonlinearbvpswhicharisefromtheproblemsincalculusofvariation
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