Skip to main content
Log in

Numerical solutions of fuzzy differential equations by using hybrid methods

  • Original Article
  • Published:
Fuzzy Information and Engineering

Abstract

In this paper, we study the numerical solution of fuzzy differential equations by using hybrid Euler method and hybrid predictor-corrector method. These methods are used to increase the accuracy and the computing speed. Also examples are presented to illustrate the computational aspects of the above methods.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abbasbandy S, Allahviranloo T (2002) Numerical solutions of fuzzy differential equations by Taylor method. Journal of Computational Methods in Applied Mathematics 2: 113–124

    MathSciNet  Google Scholar 

  2. Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences 177: 1633–1647

    Article  MathSciNet  MATH  Google Scholar 

  3. Bede B (2008) Note on “Numerical solutions of fuzzy differential equations by predictor-corrector method”. Information Sciences 178: 1917–1922

    Article  MathSciNet  MATH  Google Scholar 

  4. Buckley J J, Feuring T (2000) Fuzzy differential equations. Fuzzy Sets and Systems 110: 43–54

    Article  MathSciNet  MATH  Google Scholar 

  5. Chalco-Cano Y, Roman-Flores H (2006) On new solutions of fuzzy differential equations. Chaos, Solitons and Fractals 38: 112–129

    Article  MathSciNet  Google Scholar 

  6. Datta D P (2003) The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology. Chaos, Solitons and Fractals 17: 781–788

    Article  MathSciNet  MATH  Google Scholar 

  7. Dubois D, Prade H (2000) Fundamentals of fuzzy sets. Kluwer Academic Publishers, USA

    Book  MATH  Google Scholar 

  8. Georgiou D N, Nieto J J, Rosana Rodriguez-Lopez (2005) Initial value problems for higher-order fuzzy differential equations. Nonlinear Analysis 63: 587–600

    Article  MathSciNet  MATH  Google Scholar 

  9. Guo M, Xue X, Li R (2003) Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets and Systems 138: 601–615

    Article  MathSciNet  MATH  Google Scholar 

  10. Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets and Systems 24: 301–317

    Article  MathSciNet  MATH  Google Scholar 

  11. Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35: 389–396

    Article  MathSciNet  MATH  Google Scholar 

  12. Ma M, Friedman M, Kandel A (1999) Numerical solution of fuzzy differential equations. Fuzzy Sets and Systems 105: 133–138

    Article  MathSciNet  MATH  Google Scholar 

  13. Nieto J J, Torres A (2003) Midpoints for fuzzy sets and their application in medicine. Artificial Intelligence in Medicine 27: 81–101

    Article  Google Scholar 

  14. Pederson S, Sambandham M (2007) Numerical solution to hybrid fuzzy systems. Mathematical and Computer Modelling 45: 1133–1144

    Article  MathSciNet  MATH  Google Scholar 

  15. Pederson S, Sambandham M (2008) The Runge-Kutta method for hybrid fuzzy differential equation. Nonlinear Analysis: Hybrid Systems 2: 626–634

    Article  MathSciNet  MATH  Google Scholar 

  16. Prakash P, Kalaiselvi V (2009) Numerical solution of hybrid fuzzy differential equations by predictorcorrector method. International Journal of Computer Mathematics 86: 121–134

    Article  MathSciNet  MATH  Google Scholar 

  17. Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets and Systems 24: 319–330

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang H, Liao X, Yu J (2005) Fuzzy modeling and synchronization of hyperchaotic systems. Chaos, Solitons and Fractals 26: 835–843

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to P. Prakash or V. Kalaiselvi.

About this article

Cite this article

Prakash, P., Kalaiselvi, V. Numerical solutions of fuzzy differential equations by using hybrid methods. Fuzzy Inf. Eng. 4, 445–455 (2012). https://doi.org/10.1007/s12543-012-0126-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12543-012-0126-9

Keywords

Navigation