Skip to main content
SpringerLink
Log in

The numerical solution of linear fuzzy Fredholm integral equations of the second kind by using finite and divided differences methods

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. In this paper, we use the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind with arbitrary kernel and present some examples to illustrate this 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

Similar content being viewed by others

References

  • Abbasbandy S, Allahviranloo T (2006) The Adomian decomposition method applied to the fuzzy system of Fredholm integral equations of the second kind. Int J Uncertain Fuzziness Knowl-Bassed Syst 14:101–110

    Article  MathSciNet  MATH  Google Scholar 

  • Abbasbandy S, Babolian E, Alavi M (2007) Numerical method for solving linear Fredholm fuzzy integral equations of the second kind. Chaos Solitons Fractals 31:138–146

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2003) A comment on fuzzy linear systems. Fuzzy Sets Syst 140:554

    Article  Google Scholar 

  • 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 161:733–744

    Article  MathSciNet  MATH  Google Scholar 

  • Bede B, Gal SG (2004) Quadrature rules for integral of fuzzy-number-valued functions. Fuzzy Sets Syst 145:359–380

    Article  MathSciNet  MATH  Google Scholar 

  • Bica AM (2008) Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations. Inf Sci 178:1279–1292

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman M, Ming M, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96:201–209

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman M, Ming M, Kandel A (1999a) Numerical solutions of fuzzy differential and integral equations. Fuzzy Sets Syst 106:35–48

    Article  MATH  Google Scholar 

  • Friedman M, Ming M, Kandel A (1999b) Solutions to fuzzy integral equations with arbitrary integral kernels. Int J Approx Reason 20:249–262

    Article  MathSciNet  MATH  Google Scholar 

  • Goetschel R, Voxman W (1986) Elementary calculus. Fuzzy Sets Syst 18:31–43

    Article  MathSciNet  MATH  Google Scholar 

  • Jain MK, Iyengar SRK, Jain RK (1993) Numerical method for scientific and engineering computation. New Age International (P) Ltd

  • Ma M, Friedman M, Kandel A (1999) A new fuzzy arithmetic. Fuzzy Sets Syst 108:83–90

    Article  MathSciNet  MATH  Google Scholar 

  • Park JY, Lee SY, Jeong JU (2000) The approximate solution of fuzzy functional integral equations. Fuzzy Sets Syst 110:79–90

    Article  MathSciNet  MATH  Google Scholar 

  • Rashed MT (2004) Numerical solutions of functional integral equations. Appl Math Comput 156:507–512

    Article  MathSciNet  MATH  Google Scholar 

  • Sadeghi Goghary H, Sadeghi Goghary M (2006) Two computational methods for solving linear Fredholm fuzzy integral equations of the second kind. Appl Math Comput 182:791–796

    Article  MathSciNet  MATH  Google Scholar 

  • Wu C, Gong Z (2001) On Henstock integral of fuzzy-number-valued functions. Fuzzy Sets Syst 120:523–532

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This article has resulted from the research project supported by Islamic Azad University of Kermanshah Branch in Iran.

Author information

Authors and Affiliations

  1. Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

    N. Parandin

  2. Department of Mathematics, Central Tehran Branch, Islamic Azad University, P.O. Box 13185.768, Tehran, Iran

    M. A. Fariborzi Araghi

Authors
  1. N. Parandin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Fariborzi Araghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Parandin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parandin, N., Fariborzi Araghi, M.A. The numerical solution of linear fuzzy Fredholm integral equations of the second kind by using finite and divided differences methods. Soft Comput 15, 729–741 (2010). https://doi.org/10.1007/s00500-010-0606-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-010-0606-y

Keywords

Search

Navigation