Skip to main content
SpringerLink
Log in

Application of Legendre Wavelets for Solving a Class of Functional Integral Equations

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

In this article, an algorithm based on the Legendre wavelet for solving a special class of functional linear Volterra and Fredholm integral equations has been introduced. In this technique, numerical integration rules for discrete integral and also Legendre wavelet operational matrix of integration have benefited. Then, some numerical examples are presented to demonstrate the solubility and simplicity of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Abbasbandy S (2007) Application of Hes homotopy perturbation method to functional integral equations. Chaos Solit Fract 31:1243–1247

    Article  MathSciNet  MATH  Google Scholar 

  • Babolian E, Abbasbandy S, Fattahzadeh F (2008) A numerical method for solving a class of functional and two dimensional integral equations. Appl Math Comput 198:35–43

    MathSciNet  MATH  Google Scholar 

  • Babolian E, Fattahzadeh F (2007) Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration. Appl Math Comput 188:417–426

    MathSciNet  MATH  Google Scholar 

  • Bloom F (1980) Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory. J Math Anal Appl 73:524–542

    Article  MathSciNet  MATH  Google Scholar 

  • Cattani C, Kudreyko A (2010) Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind. Appl Math Comput 215:4164–4171

    MathSciNet  MATH  Google Scholar 

  • Delves LM, Mohamed JL (1985) Computational methods for integral equations. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Holmaker K (1993) Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones. SIAM J Math Anal 24(1):116–128

    Article  MathSciNet  Google Scholar 

  • Jafari H, Yousefi SA, Firoozjaee MA, Momani S, Khalique CM (2011) Application of Legendre wavelets for solving fractional differential equations. Comput Math Appl 62:1038–1045

    Article  MathSciNet  MATH  Google Scholar 

  • Khellat F, Yousefi SA (2006) The linear Legendre mother wavelets operational matrix of integration and its application. J Frank Inst 343:181–90

    Article  MathSciNet  MATH  Google Scholar 

  • Kyselka A (1977) Properties of systems of integro-differential equations in the statistics of polymer chains. Polym Sci USSR 19(11):2852–2858

    Article  Google Scholar 

  • Lepik U (2006) Haar wavelet method for nonlinear integro-differential equations. Appl Math Comput 176:324–333

    MathSciNet  MATH  Google Scholar 

  • Lepik U (2009) Solving fractional integral equations by the Haar wavelet method. Appl Math Comput 214:468–478

    MathSciNet  MATH  Google Scholar 

  • Liu N, Lin E-B (1998) Legendre wavelet method for numerical solutions of partial differential equations. SIAM J Math Anal 29:1040–1065

    Article  MathSciNet  Google Scholar 

  • Maleknejad K, Mirzaee F (2005) Using rationalized Haar wavelet for solving linear integra l equations. Appl Math Comput 160:579–587

    MathSciNet  MATH  Google Scholar 

  • Maleknejad K, Sohrabi S (2007) Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets. Appl Math Comput 186:836–43

    MathSciNet  MATH  Google Scholar 

  • Rashed MT (2004) Numerical solution of functional differential, integral and integro-differential equations. Appl Math Comput 156:485–492

    MathSciNet  MATH  Google Scholar 

  • Razzaghi M, Yousefi S (2001) The Legendre wavelets operational matrix of integration. Int J Syst Sci 32:495–502

    Article  MathSciNet  MATH  Google Scholar 

  • Saeedi H, Moghadam MM (2011) Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets. Appl Math Comput 16:1216–1226

    MathSciNet  MATH  Google Scholar 

  • Saeedi H, Moghadam MM, Mollahasani N, Chuev GN (2011) A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order. Commun Nonlinear Sci Num Sim 16:1154–1163

    Article  MathSciNet  MATH  Google Scholar 

  • Schiavane P, Constanda C, Mioduchowski A (2002) Integral methods in science and engineering. Birkhuser, Boston

    Google Scholar 

  • ur Rehman M, Khan RA (2011) The Legendre wavelet method for solving fractional differential equations. Commun Nonlinear Sci Numer Simul 16:4163–4173

    Article  MathSciNet  MATH  Google Scholar 

  • Yousefi SA (2006) Legendre wavelets method for solving differential equations of LaneEmden type. Appl Math Comput 181:417–422

    Google Scholar 

  • Yuanlu LI (2010) Solving a nonlinear fractional differential equation using Chebyshev wavelets. Commun Nonlinear Sci Numer Simul 15:2284–2292

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng X, Yang X (2009) Techniques for solving integral and differential equations by Legendre wavelets. Int J Syst Sci 40:1127–1137

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate University of Advanced Technology, Kerman, Iran

    Marziyeh Felahat

  2. Mathematics Department, Shahid Bahonar University of Kerman, Kerman, Iran

    Mahmoud Mohseni Moghadam & Ata Allah Askarihemmat

Authors
  1. Marziyeh Felahat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahmoud Mohseni Moghadam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ata Allah Askarihemmat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marziyeh Felahat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Felahat, M., Mohseni Moghadam, M. & Askarihemmat, A.A. Application of Legendre Wavelets for Solving a Class of Functional Integral Equations. Iran J Sci Technol Trans Sci 43, 1089–1100 (2019). https://doi.org/10.1007/s40995-018-0537-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-018-0537-5

Keywords

Search

Navigation