A New Approach for the Solution of Fuzzy Initial Value Problems Through Runge-Kutta Method

Authors

  • S. Sindu Devi Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science & Technology, Ramapuram, Chennai 440089
  • K. Ganesan Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science & Technology, Ramapuram, Chennai 440089

DOI:

https://doi.org/10.26713/jims.v12i2.1144

Keywords:

Generalized H-differentiability, Fuzzy derivatives, Fuzzy differential equations, Runge-Kutta method formula

Abstract

In this paper we propose a new approach for the solution of second order fuzzy initial value problem without converting to a system of linear fuzzy differential equations using Runge Kutta Method of fourth order under H-differentiability especially increasing length of support. Numerical examples are provided to show the stability and convergence of the proposed method with error control.

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References

Z. A. Ghanaie and M. M. Moghadam, Solving fuzzy differential equations by Runge-Kutta method, The Journal of Mathematics and Computer Science 2(2) (2011), 208 – 221, DOI: 10.22436/jmcs.002.02.01.

G. A. Anastassiou and S. G. Gal, On a fuzzy trigonometric approximation theorem of Weirstrass type, Journal of Fuzzy Mathematics 9(3) (2001), 701 – 708.

B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy number-valued functions with applications to fuzzy differential equation, Fuzzy Sets and Systems 151 (2005), 581 – 599, DOI: 10.1016/j.fss.2004.08.001.

B. Bede, I. J. Rudas and A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability Information Sciences 177 (7), 1648 – 1662, DOI: 10.1016/j.ins.2006.08.021.

S. L. Chang and L. A. Zadeh, On fuzzy mapping and control, IEEE Transactions on Systems, Man and Cybernetics 2 (1972), 30 – 34, DOI: 10.1109/TSMC.1972.5408553.

D. Dubois and H. Prade, Towards fuzzy differential calculus part 3: differential, Fuzzy Sets and Systems 8 (1982), 225 – 233, DOI: 10.1016/S0165-0114(82)80001-8.

B. Bede, I. J. Rudas and A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Information Sciences 177 (2007), 1648 – 1662, DOI: 10.1016/j.ins.2006.08.021.

F. Rabiei, F. Ismail, A. Ahmadian and S. Salahshour, Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method, Mathematical Problems in Engineering 2013 (2013), Article ID 803462, 10 pages, DOI: 10.1155/2013/803462.

T. Jayakumar, D. Maheskumar and K. Kanagarajan, Numerical solution of fuzzy differential equations by Runge-Kutta method of order five, Applied Mathematical Sciences 6(57-60) (2012), 2989 – 3002, http://m-hikari.com/ams/ams-2012/ams-57-60-2012/maheskumarAMS57-60-2012.pdf.

T. Jayakumar and T. Muthukumar, Numerical method of differential equation by Runge-Kutta method with full fuzzy initial values, MATLAB Journal 1(1) (2018), 100 – 114, https://purkh.com/index.php/mathlab/article/view/7/60.

A. Kandel and W. J. Byatt, Fuzzy process, Fuzzy Sets and Systems 4 (1980), 117 – 152, DOI: 10.1016/0165-0114(80)90032-9.

M. Friedman, M. Ma and A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and System 106 (1999), 35 – 48, DOI: 10.1016/S0165-0114(98)00355-8.

M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications 91 (1983), 552 – 558, DOI: 10.1016/0022-247X(83)90169-5

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Published

June 30, 2020

Issue

Section

Research Article

How to Cite

Devi, S. S., & Ganesan, K. (2020). A New Approach for the Solution of Fuzzy Initial Value Problems Through Runge-Kutta Method. Journal of Informatics and Mathematical Sciences, 12(2), 149-157. https://doi.org/10.26713/jims.v12i2.1144