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Issue:Numerical solution of fuzzy differential equation by Runge-Kutta method and the intuitionistic treatment

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Title of paper: Numerical solution of fuzzy differential equation by Runge-Kutta method and the intuitionistic treatment
Author(s):
S. Abbasbandy
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
abbasbandy@yahoo.com
T. Allah Viranloo
Department of Mathematics, Science and Research Branch,

Islamic Azad University, Tehran, Iran

alahviranlo@yahoo.com
Presented at: 6th ICIFS, Varna, 13—14 Sept 2002
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3, pages 43—53
Download:  PDF (4451  Kb, File info)
Abstract: In this paper numerical algorithms for solving ’fuzzy ordinary differential equations’ are considered. A scheme based on the 4th Runge-Kutta method in detail is discussed and this is followed by a complete error analysis. The algorithm is illustrated by solving some linear and nonlinear fuzzy Cauchy problems. Comments on intuitionistic fuzzy differential equations are included.
Keywords: Fuzzy differential equation, 4th Runge-Kutta method, Fuzzy Cauchy problem
AMS Classification: 34A12, 65L05
References:
  1. S.L. Chang, L.A. Zadeh, On fuzzy mapping and control, IEEE Trans, Systems Man Cybernet. 2 (1972) 30-34.
  2. D.Dubois, H. Prade, Towards fuzzy differential calculus: Part 3, differentiation, Fuzzy Sets and Systems 8 (1982) 225-233.
  3. M.L Puri, D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl. 91 (1983) 321-325.
  4. R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18 (1986) 31-43.
  5. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.
  6. O. Kaleva, The Cauchy problem for Fuzzy differential equations, Fuzzy Sets and Systems 35 (1990) 389-396.
  7. S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.
  8. R. L. Burden, J. D. Faires, Numerical Analysis, (1997)
  9. A. Ralston, P. Rabinowitz, First Course In Numerical Analysis, (1978)
  10. M. Ma, M. Friedman, A. Kandel, Numerical Solutions of fuzzy differential equations, Fuzzy Sets and Systems 105 (1999) 133-138.
  11. James J. Buckley, Thomas Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110 (2000) 43-54.
  12. K. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, (1999).
  13. K. Peeva, Intuitionistic fuzzy languages in syntactic pattern recognition, Notes on Intuitionistic Fuzzy Sets, Proceedings of the Fifth International Conference on Intuitionistic Fuzzy Sets, Sofia, 22-23 Sept. 2001, Vol. 7 (4) (2001) 77-83.
  14. K. Peeva, Resolution of composite intuitionistic fuzzy relational equations, Notes on Intuitionistic Fuzzy sets, 6(1) (2000), 15-24.
  15. K. Peeva, Min-max-fuzzy linear systems of equations, in 26th Summer School Applications of Mathematics in Engineering and Economics, B. Cheshankov, M. Todorov (Eds.), Sozopol 2000, Heron Press, 2001, 254-259.
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