Skip to main content
Erschienen in: Soft Computing 2/2015

01.02.2015 | Methodologies and Application

A new study on first-order fuzzy Fredholm–Volterra integro-differential equations by Jacobi polynomials and collocation methods

verfasst von: Sh. S. Behzadi

Erschienen in: Soft Computing | Ausgabe 2/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, the Jacobi polynomials and the collocation methods for solving first-order fuzzy linear Fredholm–Volterra integro-differential equation of the second kind under the generalized \(H\)-differentiability are introduced. The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. Finally an example shows the accuracy of these methods.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

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!

Literatur
Zurück zum Zitat Alikhani R, Bahrami F, Jabbari A (2012) Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations. Nonlinear Anal 75:1810–1821 Alikhani R, Bahrami F, Jabbari A (2012) Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations. Nonlinear Anal 75:1810–1821
Zurück zum Zitat Allahviranloo T, Khezerloo M, Ghanbari M, Khezerloo S (2010) The homotopy perturbation method for fuzzy Volterra integral equations. Int J Comput Cognition 8:31–37 Allahviranloo T, Khezerloo M, Ghanbari M, Khezerloo S (2010) The homotopy perturbation method for fuzzy Volterra integral equations. Int J Comput Cognition 8:31–37
Zurück zum Zitat Allahviranloo T, Khalilzadeh N, Khezerloo S (2011) Solving linear Fredholm fuzzy integral equations of the second kind by modified trapezoidal method. J Appl Math 7:25–37 Islamic Azad University of Lahijan Allahviranloo T, Khalilzadeh N, Khezerloo S (2011) Solving linear Fredholm fuzzy integral equations of the second kind by modified trapezoidal method. J Appl Math 7:25–37 Islamic Azad University of Lahijan
Zurück zum Zitat Allahviranloo T, Behzadi ShS (2013) The use of airfoil and Chebyshev polynomials methods for solving fuzzy Fredholm integro-differential equations with Cauchy kernel. Soft Comput. doi:10.1007/s00500-013-1173-9 Allahviranloo T, Behzadi ShS (2013) The use of airfoil and Chebyshev polynomials methods for solving fuzzy Fredholm integro-differential equations with Cauchy kernel. Soft Comput. doi:10.​1007/​s00500-013-1173-9
Zurück zum Zitat Babolian E, Sadeghi Goghary H, Abbasbandy S (2005) Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method. Appl Math Comput 161:733–744CrossRefMATHMathSciNet Babolian E, Sadeghi Goghary H, Abbasbandy S (2005) Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method. Appl Math Comput 161:733–744CrossRefMATHMathSciNet
Zurück zum Zitat Bede B, Gal SG (2005) Generalizations of differentiability of fuzzy-number valued function with application to fuzzy differential equations. Fuzzy Sets Syst 151:581–599CrossRefMATHMathSciNet Bede B, Gal SG (2005) Generalizations of differentiability of fuzzy-number valued function with application to fuzzy differential equations. Fuzzy Sets Syst 151:581–599CrossRefMATHMathSciNet
Zurück zum Zitat Behzadi ShS, Allahviranloo T, Abbasbandy S (2012) Solving fuzzy second-order nonlinear Volterra–Fredholm integro-differential equations by using Picard method. Neural Comput Appl. doi:10.1007/s00521-012-0926-1 Behzadi ShS, Allahviranloo T, Abbasbandy S (2012) Solving fuzzy second-order nonlinear Volterra–Fredholm integro-differential equations by using Picard method. Neural Comput Appl. doi:10.​1007/​s00521-012-0926-1
Zurück zum Zitat Behzadi ShS, Allahviranloo T, Abbasbandy S (2013) The use of fuzzy expansion method for solving fuzzy linear Volterra-Fredholm integral equations. J Intell Fuzzy Syst. doi:10.3233/IFS-130861 Behzadi ShS, Allahviranloo T, Abbasbandy S (2013) The use of fuzzy expansion method for solving fuzzy linear Volterra-Fredholm integral equations. J Intell Fuzzy Syst. doi:10.​3233/​IFS-130861
Zurück zum Zitat Behzadi ShS (2011) Solving fuzzy nonlinear Volterra–Fredholm integral equations by using homotopy analysis and Adomian decomposition methods. J Fuzzy Set Valued Anal. doi:10.5899/2011/jfsva-000671-13 Behzadi ShS (2011) Solving fuzzy nonlinear Volterra–Fredholm integral equations by using homotopy analysis and Adomian decomposition methods. J Fuzzy Set Valued Anal. doi:10.​5899/​2011/​jfsva-000671-13
Zurück zum Zitat Chalco-Cano Y, Romn-Flores H (2006) On new solutions of fuzzy differential equations. Chaos Soliton Fractals 38:112–119 Chalco-Cano Y, Romn-Flores H (2006) On new solutions of fuzzy differential equations. Chaos Soliton Fractals 38:112–119
Zurück zum Zitat Dubois D, Prade H (1980) Theory and application. Academic Press, New York Dubois D, Prade H (1980) Theory and application. Academic Press, New York
Zurück zum Zitat Friedman M, Ma M, Kandel A (1996) Numerical methods for calculating the fuzzy integral. Fuzzy Sets Syst 83:57–62 Friedman M, Ma M, Kandel A (1996) Numerical methods for calculating the fuzzy integral. Fuzzy Sets Syst 83:57–62
Zurück zum Zitat Jahantigh M, Allahviranloo T, Otadi M (2008) Numerical solution of fuzzy integral equation. Appl Math Sci 2:33–46MATHMathSciNet Jahantigh M, Allahviranloo T, Otadi M (2008) Numerical solution of fuzzy integral equation. Appl Math Sci 2:33–46MATHMathSciNet
Zurück zum Zitat Kauffman A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and application. Van Nostrand Reinhold, New York Kauffman A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and application. Van Nostrand Reinhold, New York
Zurück zum Zitat Khorasany M, Khezerloo S, Yildirim A (2011) Numerical method for solving fuzzy Abel integral equations, World. Appl Sci J 13:2350–2354 Khorasany M, Khezerloo S, Yildirim A (2011) Numerical method for solving fuzzy Abel integral equations, World. Appl Sci J 13:2350–2354
Zurück zum Zitat Li X, Tang T (2012) Convergence analysis of Jacobi spectral collocation methods for Abel–Volterra integral equations of second kind. Front Math China 7:69–84CrossRefMATHMathSciNet Li X, Tang T (2012) Convergence analysis of Jacobi spectral collocation methods for Abel–Volterra integral equations of second kind. Front Math China 7:69–84CrossRefMATHMathSciNet
Zurück zum Zitat Mikaeilvand N, Khakrangin S, Allahviranloo T (2011) Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method, EUSFLAT- LFA, pp 891–896 Mikaeilvand N, Khakrangin S, Allahviranloo T (2011) Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method, EUSFLAT- LFA, pp 891–896
Zurück zum Zitat Molabahrami A, Shidfar A, Ghyasi A (2011) An analytical method for solving linear Fredholm fuzzy integral equations of the second kind. Comput Math Appl 61:2754–2761CrossRefMATHMathSciNet Molabahrami A, Shidfar A, Ghyasi A (2011) An analytical method for solving linear Fredholm fuzzy integral equations of the second kind. Comput Math Appl 61:2754–2761CrossRefMATHMathSciNet
Zurück zum Zitat Mosleh M, Otadi M (2011) Numerical solution of fuzzy integral equations using Bernstein polynomials. Aust J Basic Appl Sci 5:724–728 Mosleh M, Otadi M (2011) Numerical solution of fuzzy integral equations using Bernstein polynomials. Aust J Basic Appl Sci 5:724–728
Zurück zum Zitat Salahshour S, Abbasbandy S (2014) A comment on global solutions for nonlinear fuzzy fractional integral and integrodifferential equations. Commun Nonlinear Sci Numer Simul 19:1256–1258CrossRefMathSciNet Salahshour S, Abbasbandy S (2014) A comment on global solutions for nonlinear fuzzy fractional integral and integrodifferential equations. Commun Nonlinear Sci Numer Simul 19:1256–1258CrossRefMathSciNet
Zurück zum Zitat Sugeno M (1974) Theory of fuzzy integrals and its application. PhD thesis, Tokyo Institute of Technology Sugeno M (1974) Theory of fuzzy integrals and its application. PhD thesis, Tokyo Institute of Technology
Zurück zum Zitat Vu H, Dong LS, Hoa NV (2014) Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. J Intell Fuzzy Syst. doi:10.3233/IFS-131116 Vu H, Dong LS, Hoa NV (2014) Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. J Intell Fuzzy Syst. doi:10.​3233/​IFS-131116
Zurück zum Zitat Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353 Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Metadaten
Titel
A new study on first-order fuzzy Fredholm–Volterra integro-differential equations by Jacobi polynomials and collocation methods
verfasst von
Sh. S. Behzadi
Publikationsdatum
01.02.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 2/2015
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-014-1261-5

Weitere Artikel der Ausgabe 2/2015

Soft Computing 2/2015 Zur Ausgabe