Result: Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations
Title:
Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations
Authors:
Source:
Mathematical and computer modelling. 54(9-10):2040-2050
Publisher Information:
Kidlington: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 31 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations algébriques et transcendantes non linéaires, Nonlinear algebraic and transcendental equations, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Méthodes de calcul scientifique (y compris calcul symbolique, calcul algébrique), Methods of scientific computing (including symbolic computation, algebraic computation), Algèbre linéaire numérique, Numerical linear algebra, Algebra lineal numérica, Analyse assistée, Computer aided analysis, Análisis asistido, Analyse numérique, Numerical analysis, Análisis numérico, Calcul variationnel, Variational calculus, Cálculo de variaciones, Equation algébrique, Algebraic equation, Ecuación algebraica, Equation différentielle, Differential equation, Ecuación diferencial, Equation non linéaire, Non linear equation, Ecuación no lineal, Equation ordre 1, First order equation, Ecuación orden 1, Equation transcendante, Transcendental equation, Ecuación trascendente, Inversion matrice, Matrix inversion, Inversión matriz, Itération, Iteration, Iteracción, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Modèle mathématique, Mathematical model, Modelo matemático, Multiplicateur Lagrange, Lagrange multiplier, Multiplicador Lagrange, Méthode directe, Direct method, Método directo, Méthode itérative, Iterative method, Método iterativo, Méthode optimisation, Optimization method, Método optimización, Programmation mathématique, Mathematical programming, Programación matemática, Système linéaire, Linear system, Sistema lineal, Système non linéaire, Non linear system, Sistema no lineal, Système équation, Equation system, Sistema ecuación, 14C20, 34XX, 49R50, 65F05, 65F10, 65H10, 65K10, 65Kxx, 65Lxx, Higher-order differential equations, Iterative solutions, Lagrange multipliers, Restricted variations, Systems of differential equations, Variational iteration method
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Selçuk University, 42697 Konya, Turkey
Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey
Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey
ISSN:
0895-7177
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24482998
Database:
PASCAL Archive
Further Information
In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses restricted variations only for nonlinear terms by generalising the Lagrange multipliers. Consequently, this allows us to use the well known, but ignored, theory of linear ODEs for computing the matrix-valued Lagrange multipliers. In order to validate the newly proposed approach in solving linear and nonlinear systems of differential equations, illustrative examples are presented: it turns out that the use of the generalised Lagrange multipliers is more reliable and efficient.