Abstract
In this paper the fuzzy improved Runge–Kutta method of order four for solving first-order fuzzy differential equations is proposed. The scheme is two step in nature and is based on the fourth-order improved Runge–Kutta method for solving first-order ordinary differential equations. The numerical examples are tested to illustrate the efficiency of method.
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References
Chang, S.L., Zadeh, L.A.: On fuzzy mapping and control. IEEE Trans. Syst. Man Cybern. 2, 30–34 (1972)
Dubois, D., Prade, H.: Towards fuzzy differential calculus part 3: differentiation. Fuzzy Set. Syst. 8, 225–233 (1982)
Abbasbandy, S., Allahviranloo, T.: Numerical solution of fuzzy differential equations by Taylor method. J. Comput. Methods Appl. Math. 2, 113–124 (2002)
Seikkala, S.: On the fuzzy initial value problem. Fuzzy Set. Syst. 24, 319–330 (1987)
Ahmad, M.Z., Hasan, M.K.: Anew fuzzy version of Euler’s method for solving differential equations with fuzzy initial values. Sains Malays. 40(6), 651–657 (2011)
Rabiei, F., Ismail, F.: Improved Runge–Kutta methods for solving ordinary differential equations. Sains Malays. 42(11), 1679–1687 (2013)
Akbarzadeh Ghanaie, Z., Mohseni Moghadam, M.: Solving fuzzy differential equations by Runge–Kutta method. J. Math. Comput. Sci. 2(2), 208–221 (2011)
Chalco-Cano, Y., Roman-Flores, H.: On new solution of fuzzy differential equations. Chaos Solitons Fractals 38, 112–119 (2008)
Friedman, M., Ma, M., Kandel, A.: Numerical solutions of fuzzy differential equations. Fuzzy Set. Syst. 105, 133–138 (1999)
Solaymani Fard, O., Ghal-eh, N.: Numerical solution for linear system of first order fuzzy differential equations with fuzzy constant coefficients. Inform. Sci. 181, 4765–4779 (2011)
Acknowledgment
This research has been financed by University Putra Malaysia using Universiti Putra grant with project number GP-IPM/2013/9405100 at the Institute For Mathematical Research, Universiti Putra Malaysia.
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Rabiei, F., Ismail, F., Emadi, S. (2016). Solving Fuzzy Differential Equation Using Fourth-Order Four-Stage Improved Runge–Kutta Method. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.18_15
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DOI: https://doi.org/10.5176/2251-1911_CMCGS14.18_15
Publisher Name: Springer, Cham
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