Abstract
In this paper, solving fuzzy ordinary differential equations of the nth order by Runge–Kutta method hav been done. In this following, the convergence of the proposed method is proved. The proposed method is illustrated by numerical examples.
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References
Buckley JJ, Feuring T (2000) Fuzzy differential equations. Fuzzy Sets Syst 110:43–54
Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317
Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Sets Syst 35:389–396
Nieto JJ (1999) The Cauchy problem for continuous fuzzy differential equations. Fuzzy Sets Syst 102:259–262
Ouyang H, Wu Y (1989) On fuzzy differential equations. Fuzzy Sets Syst 32:321–325
Roman-Flores H, Rojas-Medar M (2002) Embedding of level-continuous fuzzy sets on Banach spaces. Inf Sci 144:227–247
Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24:319–330
Bede B, Gal SG (2005) Generalizations of the differntiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581–599
Diamond P (2000) Stability and periodicity in fuzzy differential equations. IEEE Trans Fuzzy Syst 8:583–590
Diamond P (2002) Brief note on the variation of constants formula for fuzzy differential equations. Fuzzy Sets Syst 129:65–71
Georgiou DN, Nieto JJ, Rodriguez-Lopez R (2005) Initial value problems for higher-order fuzzy differential equations. Nonlinear Anal 63:587–600
Nieto JJ, Rodriguez-Lopez R (2006) Bounded solutions for fuzzy differential and integral equations. Chaos Solitons Fractals 27:1376–1386
Abbasbandy S, Allahviranloo T (2002) Numerical solution of fuzzy differential equation by Runge-Kutta method. J Sci Teacher Training Univ 1(3 & 4), Fall 2001 and Winter 2002
Abbasbandy S, Allahviranloo T (2002) Numerical solutions of fuzzy differential equations by Taylor method. J Comput Methods Appl Math 2:113–124
Abbasbandy S, Allahviranloo T, Lopez-Pouso O, Nieto JJ (2004) Numerical methods for fuzzy differential inclusions. J Comput Math Appl 48:1633–1641
Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Inf Sci 177:1633–1647
Allahviranloo T, Ahmady E, Ahmady N (2008) Nth-order fuzzy linear differential equations. Inf Sci 178:1309–1324
Allahviranloo T, Kiani NA, Motamedi N (2009) Solving fuzzy differential equations by differential transformation method. Inf Sci 179:956–966
Ma Ming, Friedman M, Kandel A (1999) Numerical solutions of fuzzy differential equations. Fuzzy Sets Syst 105:133–138
Friedman M, Ming M, Kandel A (1999) Numerical solutions of fuzzy differential and integral equations. Fuzzy Sets Syst 106:35–48
Khastan A, Ivaz K (2009) Numerical solution of fuzzy differential equations by Nystrom method. Chaos Solitons Fractals 41:859–868
Pederson S, Sambandham M (2008) The Runge-Kutta method for hybrid fuzzy differential equations. Nonlinear Anal Hybrid Syst 2:626–634
Palligkinis SCh, Papageorgiou G, Famelis ITh (2009) Runge-Kutta methods for fuzzy differential equations. Appl Math Comput 209:97–105
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This article has resulted from the research project supported by Islamic Azad University of Kermanshah Branch in Iran.
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Parandin, N. Numerical solution of fuzzy differential equations of nth-order by Runge–Kutta method. Neural Comput & Applic 21 (Suppl 1), 347–355 (2012). https://doi.org/10.1007/s00521-012-0928-z
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DOI: https://doi.org/10.1007/s00521-012-0928-z