Abstract

In this paper we define the fuzzy differential equation of the first order and solve this equation by numerical solution in Runge-Kutta Method. We introduce an example to solve the problem by using this method, and applied in matlab computer software.

Keywords

References

[1] L. A. Zadeh, “Fuzzy sets”, Information and Control, Vol.8, pp. 338-353, (1965).
[2] Kaleva O., Fuzzy differential equations, Fuzzy Sets and Systems,24, 301-317 (1987).
[3] Kaleva O., The Cauchy problem for fuzzy differential equations,Fuzzy Sets and Systems, 35, 389-396 (1990).
[4] J.J. Buckley and E.Eslami, Introduction to Fuzzy Logic andFuzzy Sets, PhysicaVerlag, Heidelberg, Germany, (2001).
[5] S. Abbasbandy and T. Allah Viranloo, “Numericalsolutionof fuzzy differential equation,” Mathematical & ComputationalApplications, vol. 7, no. 1, pp. 41–52, (2002).
[6] S. Abbasbandy, T. A. Viranloo, ´ O. L´opez-Pouso, and J.Nieto,“Numerical methods for fuzzy differential inclusions,”Computers & Mathematics with Applications, vol. 48, no. 10-11,pp. 1633–1641, (2004).
[7] T. Allahviranloo, N. Ahmady, and E. Ahmady, “Numericalsolution of fuzzy differential equations by predictor-correctormethod,” Information Sciences, vol. 177, no. 7, pp. 1633–1647,(2007).
[8] T. Allahviranloo, E. Ahmady, and N. Ahmady, “th-order fuzzylinear differential equations,” Information Sciences, vol. 178, no.5, pp. 1309–1324, (2008).
[9] Khaki M., Ganji D. D., Analytical solutions of Nano boundarylayer flows by using he’s homotopy perturbation method,Mathematical and Computational Applications, 15, No. 5, 962-966, (2010).
[10] M. T.Malinowski, “Existence theorems for solutions to randomfuzzy differential equations,” Nonlinear Analysis: Theory,Methods & Applications, vol. 73, no. 6, pp. 1515–1532, (2010).
[11] O. SolaymaniFard and T. AliAbdoliBidgoli, “The Nystrommethod for hybrid fuzzy differential equation IVPs,” Journal ofKing Saud University Science, vol. 23, pp. 371–379, (2011).
[12] M. BarkhordariAhmadi and M. Khezerloo, “Fuzzy bivariateChebyshev method for solving fuzzy VolterraFredholm integralequations,” International Journal of Industrial Mathematics,vol. 3, pp. 67–77, (2011).
[13] H. Kim and R. Sakthivel, “Numerical solution of hybrid fuzzydifferential equations using improved predictor-corrector method,”Communications in Nonlinear Science and NumericalSimulation,vol. 17, no. 10, pp. 3788–3794, (2012).
[14] B. Ghazanfari and A. Shakerami, “Numerical solutions of fuzzydifferential equations by extended Runge-Kutta-like formulaeof order 4,” Fuzzy Sets and Systems, vol. 189, pp. 74–91, (2012).
[15] S. Salahshour, T. Allahviranloo, S. Abbasbandy, andD. Baleanu,“Existence and uniqueness results for fractional differentialequations with uncertainty,” Advances in Difference Equations,vol. 2012, 112 pages, (2012).
[16] S. Salahshour, T. Allahviranloo, and S. Abbasbandy, “Solvingfuzzy fractional differential equations by fuzzy Laplacetransforms,”Communications in Nonlinear Science andNumericalSimulation, vol. 17, no. 3, pp. 1372–1381, (2012).
[17] S. Ziari, R. Ezzati, and S. Abbasbandy,“Numerical solution oflinear fuzzy fredholm integral equations of the second kind usingfuzzy Haar wavelet,” in Advances in Computational Intelligence,vol. 299of Communications in Computer and InformationScience,pp. 79– 89, Springer, New York, NY, USA, (2012).
[18] T. Jayakumar, D. Maheskumar and K. Kanagarajan, Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method of Order Five, Applied Mathematical Sciences,Vol. 6, no. 60, 2989 – 3002,(2012).
[19] A. M. Bertone, R. M. Jafelice, L. C. de Barros, and R. C.Bassanezi, “On fuzzy solutions for partial differentialequations”Fuzzy Sets and Systems, vol. 219, pp. 68–80, (2013).
[20] M. Mazandarani and A. V. Kamyad, “Modified fractional Eulermethod for solving fuzzy fractional initial value problem”Communications inNonlinear Science andNumerical Simulation,vol. 18, no. 1, pp. 12–21,(2013).