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.
Similar content being viewed by others
References
Abbasbandy S, Allahviranloo T (2002) Numerical solutions of fuzzy differential equations by Taylor method. Journal of Computational Methods in Applied Mathematics 2: 113–124
Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences 177: 1633–1647
Bede B (2008) Note on “Numerical solutions of fuzzy differential equations by predictor-corrector method”. Information Sciences 178: 1917–1922
Buckley J J, Feuring T (2000) Fuzzy differential equations. Fuzzy Sets and Systems 110: 43–54
Chalco-Cano Y, Roman-Flores H (2006) On new solutions of fuzzy differential equations. Chaos, Solitons and Fractals 38: 112–129
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
Dubois D, Prade H (2000) Fundamentals of fuzzy sets. Kluwer Academic Publishers, USA
Georgiou D N, Nieto J J, Rosana Rodriguez-Lopez (2005) Initial value problems for higher-order fuzzy differential equations. Nonlinear Analysis 63: 587–600
Guo M, Xue X, Li R (2003) Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets and Systems 138: 601–615
Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets and Systems 24: 301–317
Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35: 389–396
Ma M, Friedman M, Kandel A (1999) Numerical solution of fuzzy differential equations. Fuzzy Sets and Systems 105: 133–138
Nieto J J, Torres A (2003) Midpoints for fuzzy sets and their application in medicine. Artificial Intelligence in Medicine 27: 81–101
Pederson S, Sambandham M (2007) Numerical solution to hybrid fuzzy systems. Mathematical and Computer Modelling 45: 1133–1144
Pederson S, Sambandham M (2008) The Runge-Kutta method for hybrid fuzzy differential equation. Nonlinear Analysis: Hybrid Systems 2: 626–634
Prakash P, Kalaiselvi V (2009) Numerical solution of hybrid fuzzy differential equations by predictorcorrector method. International Journal of Computer Mathematics 86: 121–134
Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets and Systems 24: 319–330
Zhang H, Liao X, Yu J (2005) Fuzzy modeling and synchronization of hyperchaotic systems. Chaos, Solitons and Fractals 26: 835–843
Author information
Authors and Affiliations
Corresponding authors
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12543-012-0126-9