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A NUMERICAL METHOD OF FUZZY DIFFERENTIAL EQUATIONS

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초록

In this paper, we propose a numerical method to solve fuzzy differential equations. Numerical experiments show that when the step size is small, the new method has significantly good approximate solutions of fuzzy differential equation. Graphical representation of fuzzy solutions in three-dimension is also provided as a reference of visual convergence of the solution sequence.

Abstract

In this paper, we propose a numerical method to solve fuzzy differential equations. Numerical experiments show that when the step size is small, the new method has significantly good approximate solutions of fuzzy differential equation. Graphical representation of fuzzy solutions in three-dimension is also provided as a reference of visual convergence of the solution sequence.

참고문헌 (15)

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  3. M. Bayrak, "Numerical solution of fuzzy differential equations by Milne's predictor-corrector method", Math. Sci. Appl. E-Notes, 3, pp.137~153 (2015)
  4. R.L. Burden, "Numerical Analysis" (2010), Brooks Cole
  5. M. Hosseini, "Numerical solution of fuzzy differential equa-tions by variational iteration method", Int. J. Fuzzy Syst, 18, pp.875~882 (2016)
  6. H. Jafari, "The Laplace decomposition method for solving n-th order fuzzy differential equations", Ann. Fuzzy Math. Inform, 7, pp.653~660 (2014)
  7. 전윤배, "AN ACCELERATING SCHEME OF CONVERGENCE TO SOLVE FUZZY NON-LINEAR EQUATIONS", 순수 및 응용수학, 24(1), pp.45~51 (2017), 한국수학교육학회
  8. O. Kaleva, "Fuzzy differential equations", Fuzzy Sets and Systems, 24, pp.301~317 (1987)
  9. O. Kichmarenko, "Partial averaging of fuzzy differential equations with maxima", Adv. Dyn. Syst. Appl, 6, pp.199~207 (2011)
  10. M. Puri, "Differentials of fuzzy functions", J. Math. Anal. Appl, 91, pp.552~558 (1983)
  11. F. Rogers, "Fuzzy nonlinear optimization for the linear fuzzy real number system", Internat. Math. Forum, 4, pp.587~596 (2009)
  12. G.K. Saha, "A new approach to solve fuzzy non-linear equations using fixed point iteration algorithm", J. Bangladesh Math. Soc, 32, pp.15~21 (2012)
  13. G.K. Saha, "Solution of fuzzy non-linear equation using bisection algorithm", Dhaka Univ. J. Sci, 61, pp.53~58 (2013)
  14. C. Yang, "Numerical solution of fuzzy differential equations by hybrid predictor-corrector method", J. Comput. Anal. Appl, 13, pp.743~755 (2011)
  15. L.A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)

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