Akbari–Ganji's Method

Modeling of nonlinear differential equations analytically is rather more difficult compared to solving linear differential equations. In this regard, the Akbari‐lGanji's method (AGM) may be considered as a powerful algebraic (semi‐analytic) approach for solving such problems. In the AGM, initia...

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Vydáno v:Advanced Numerical and Semi-Analytical Methods for Differential Equations s. 103 - 110
Hlavní autoři: Dilleswar Rao, Tharasi, Mahato, Nisha, Karunakar, Perumandla, Chakraverty, Snehashish
Médium: Kapitola
Jazyk:angličtina
Vydáno: United States John Wiley & Sons, Incorporated 2019
John Wiley & Sons, Inc
Témata:
Akbari‐Ganji's method
Duffing equations
Helmholtz equations
nonlinear ordinary differential equations
semi‐analytic approach
ISBN:9781119423423, 1119423422
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Abstract Modeling of nonlinear differential equations analytically is rather more difficult compared to solving linear differential equations. In this regard, the Akbari‐lGanji's method (AGM) may be considered as a powerful algebraic (semi‐analytic) approach for solving such problems. In the AGM, initially a solution function consisting of unknown constant coefficients is assumed satisfying the differential equation and the initial conditions (IC). Then, the unknown coefficients are computed using algebraic equations obtained with respect to IC and their derivatives. This chapter illustrates the basic notion of nonlinear differential equation and its solution procedure. It presents the detailed illustration of the AGM approach for solving second‐order unforced and forced nonlinear ordinary differential equations. The chapter also illustrates the efficiency of the procedure using unforced and forced nonlinear differential equations with respect to Helmholtz and Duffing equations, respectively.
AbstractList Modeling of nonlinear differential equations analytically is rather more difficult compared to solving linear differential equations. In this regard, the Akbari‐lGanji's method (AGM) may be considered as a powerful algebraic (semi‐analytic) approach for solving such problems. In the AGM, initially a solution function consisting of unknown constant coefficients is assumed satisfying the differential equation and the initial conditions (IC). Then, the unknown coefficients are computed using algebraic equations obtained with respect to IC and their derivatives. This chapter illustrates the basic notion of nonlinear differential equation and its solution procedure. It presents the detailed illustration of the AGM approach for solving second‐order unforced and forced nonlinear ordinary differential equations. The chapter also illustrates the efficiency of the procedure using unforced and forced nonlinear differential equations with respect to Helmholtz and Duffing equations, respectively.
Author Karunakar, Perumandla
Dilleswar Rao, Tharasi
Mahato, Nisha
Chakraverty, Snehashish
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References Sheikholeslami, Ganji (c09-cit-0004) 2018
Hermann, Seravi (c09-cit-0002) 2016
Akbari, Ganji, Nimafar, Ahmadi (c09-cit-0003) 2014; 9
Momani, Erjaee, Alnasr (c09-cit-0007) 2009; 58
Fucik, Kufner (c09-cit-0001) 2014; 2
Ganji, Talarposhti (c09-cit-0006) 2017
Akbari (c09-cit-0005) 2015
Yusufoğlu (c09-cit-0008) 2006; 177
References_xml – year: 2016
  ident: c09-cit-0002
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– volume: 58
  start-page: 2209
  issue: 11–12
  year: 2009
  end-page: 2220
  ident: c09-cit-0007
  article-title: The modified homotopy perturbation method for solving strongly nonlinear oscillators
  publication-title: Computers and Mathematics with Applications
– volume: 177
  start-page: 572
  issue: 2
  year: 2006
  end-page: 580
  ident: c09-cit-0008
  article-title: Numerical solution of Duffing equation by the Laplace decomposition algorithm
  publication-title: Applied Mathematics and Computation
– year: 2015
  ident: c09-cit-0005
  article-title: Nonlinear Dynamic in Engineering by Akbari‐Ganji's Method
– volume: 2
  year: 2014
  ident: c09-cit-0001
  article-title: Nonlinear Differential Equations
– year: 2017
  ident: c09-cit-0006
  article-title: Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer
– volume: 9
  start-page: 390
  issue: 4
  year: 2014
  end-page: 401
  ident: c09-cit-0003
  article-title: Significant progress in solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM approach
  publication-title: Frontiers of Mechanical Engineering
– year: 2018
  ident: c09-cit-0004
  article-title: Applications of Semi‐Analytical Methods for Nanofluid Flow and Heat Transfer
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Snippet Modeling of nonlinear differential equations analytically is rather more difficult compared to solving linear differential equations. In this regard, the...
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StartPage 103
SubjectTerms Akbari‐Ganji's method
Duffing equations
Helmholtz equations
nonlinear ordinary differential equations
semi‐analytic approach
Title Akbari–Ganji's Method
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