Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
On Asymptotic Behavior of Blow-Up Solutions to Higher-Order Differential Equations with General Nonlinearity Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Variational Iteration Method for Solving Problems with Integral Boundary Conditions

Authors : Ahcene Merad, Samir Hadid

Published in: Differential and Difference Equations with Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this work, Variational Iteration Method is employed to solve parabolic partial differential equations subject to initial and nonlocal inhomogeneous boundary conditions of integral type. Since nonlocal boundary conditions considerably complicate the application of standard functional and numerical techniques, equations having such conditions are first transformed to local (classical) boundary conditions Then they are solved by Variational Iteration Method.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter The Common Descent of Biological Shape Description and Special Functions
next chapter Kirchhoff-Type Boundary-Value Problems on the Real Line
Literature
1.
Cannon, J.R.: The solution of the heat equation subject to the specification of energy. Quart. Appl. Math. 21, 155–160 (1963)MathSciNetCrossRef
2.
Cannon, J.R., Perez, E.S., Vanderhoek, J.A.: Galerkin procedure for the diffusion equation subject to the specification of mass. Sia. J. Numer. Anal. 24, 499–515 (1987)MathSciNetCrossRef
3.
Kamynin, N.I.: A boundary value problem in the theory of the heat condition with non classical boundary condition. Comput. Math. phys. 4, 33–59 (1964)CrossRef
4.
Choi, Y.S., Chan, K.Y.: A parabolic equation with nonlocal boundary conditions arising from electrochemistry. Nonlin. Anal. 18, 317–331 (1992)MathSciNetCrossRef
5.
6.
Samarskii, A.A.: Some problems in differential equations theory. Differ. Uravn. 16, 1221–1228 (1980)MathSciNet
7.
Batten, J., George, W.: Second-order correct boundary condition for the numerical solution of the mixed boundary problem for parabolic equation. Math. Comput. 17, 405–413 (1963)MathSciNetCrossRef
8.
Bouziani, A., Benouar, N.E.: Mixed problem with integral conditions for third order parabolic equation. Kob. J. Math. 15, 47–58 (1998)MathSciNetMATH
9.
Bouziani, A.: Problèmes mixtes avec conditions inté grales pour quelques équations aux dérivées partielles, Ph.D. thesis, Constantine University (1996)
10.
Bouziani, A.: Mixed problem with boundary integral conditions for a certain parabolic equation. J. Appl. Math. Stochastic Anal. 09(3), 323–330 (1996)MathSciNetCrossRef
11.
Bouziani, A., Benouar, N.: Sur un problème mixte avec uniquement des conditions aux limites intégrales pour une classe d’é quations paraboliques. Maghreb Mathematical Review 9(1–2), 55–70 (2000)
12.
Bouziani, A., Merad, A.: The Laplace transform method for on-dimonsional hyperbolic equation with purely integral conditions. Romanian J. Math. Comput. Sci. 3(2), 191–204 (2013)
13.
Beïlin, S.A.: Existence of solutions for one-dimentional wave nonlocal conditions. Electron. J. Differ. Equ. 76, 1–8 (2001)MathSciNet
14.
Ekolin, G.: Finite difference methods for a nonlocal boundary value problem for the heat equation. BIT 31, 245–261 (1991)MathSciNetCrossRef
15.
Ionkin, N.I.: Solution of a boundary-value problem in heat condition with a nonclassical boundary condition. Differ. Uravn. 13, 294–304 (1977)MATH
16.
Javidi, M.: The mol solution for the one-dimensional heat equation subject to nonlocal conditions. Int. Math. Forum 12, 597–602 (2006)CrossRef
17.
Yurchuk, N.I.: Mixed problem with an integral condition for certain parabolic equations. Differ. Equ. 22, 1457–1463 (1986)MATH
18.
He, J.H.: Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114, 115–123 (2000)MathSciNetMATH
19.
Odibat, Z.M., Momani, S.: Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear SciNumer. Simul. 7(1), 27–34 (2006)
20.
Bildik, N., Konuralp, A.: The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. Int. J. Nonlinear SciNumer. Simul. 7(1), 65–70 (2006)MathSciNetMATH
21.
Bouziani, A.: Strong solution of a mixed problem with a nonlocal condition for a class of hyperbolic equations. Acad. Roy. Belg. Bull. Cl. Sci. 8, 53–70 (1997)MathSciNetMATH
22.
Bouziani, A.: Strong solution to an hyperbolic evolution problem with nonlocal boundary conditions. Maghreb Math. Rev. 9(1–2), 71–84 (2000)MathSciNet
23.
Bouziani, A.: On the quasi static flexur of thermoelastic rod. Commun. Appl. Anal. Theory Appl. 6(4), 549–568(2002)
24.
Bouziani, A.: Initial-boundary value problem with nonlocal condition for a viscosity equation. Int. J. Math. Math. Sci. 30(6), 327–338 (2002)MathSciNetCrossRef
25.
Bouziani, A.: On the solvabiliy of parabolic and hyperbolic problems with a boundary integral condition. Int. J. Math. Math. Sci. 31, 435–447 (2002)MathSciNetCrossRef
26.
Bouziani, A.: On a class of nonclassical hyperbolic equations with nonlocal conditions. J. Appl. Math. Stoch. Anal. 15(2), 136–153 (2002)MathSciNetCrossRef
27.
Bouziani, A.: Mixed problem with only integral boundary conditions for an hyperbolic equation. Int. J. Math. Math. Sci. 26, 1279–1291 (2004)MathSciNetCrossRef
28.
Bouziani, A., Benouar, N.: Problème mixte avec conditions intégrales pour une classe d’équations hyperboliques. Bull. Belg. Math. Soc. 3, 137–145 (1996)MathSciNetMATH
29.
Merad, A., Marhoune, A.L.: Strong solution for a high order boundary value problem with integral condition. Turk. J. Math. 37(3), 1–9 (2013)MathSciNetMATH
30.
Merad, A., Bouziani, A.: Numerical solution for parabolic equation with nonlocal conditions. TJMM 5(2), 121–127 (2013)MathSciNetMATH
31.
Biazar, J., Ghazvini, H.: An analytic approximation to the solution of a wave equation by a variational iteration method. Appl. Math. Lett. 21, 780–785 (2008)MathSciNetCrossRef
32.
Yousefi, S.A., Dehghan, M.: He’svariational iteration method for solving nonlinear mixed Volterra - Fredholm integral equations. Comput. Math. Appl. 58, 2172–2176 (2009)MathSciNetCrossRef
33.
Tatari, M., Dehghan, M.: Improvement of He’svariational iteration method for solving systems of differential equations. Comput. Math. Appl. 58, 2160–2166 (2009)MathSciNetCrossRef
34.
Metadata
Title
Variational Iteration Method for Solving Problems with Integral Boundary Conditions
Authors
Ahcene Merad
Samir Hadid
Copyright Year
2018
Book
Differential and Difference Equations with Applications

Print ISBN: 978-3-319-75646-2

Electronic ISBN: 978-3-319-75647-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-75647-9_11

Premium Partner

    Image Credits