This study discusses a numerical methods for hybrid fuzzy differential equations by fifth order RK Nystrom Method for fuzzy differential equations. We prove the convergence result and give numerical examples to illustrate the theory.
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[2] D. Dubois and H.Prade, Towards Fuzzy Differential Calculus: Part 3, Differentiation, Fuzzy Sets and System, 8 (1982,) 225–233.
[3] M. L. Puri, D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983), 321–325.
[4] R. Goetschel, W.Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), 31–43.
[5] A. Kandel, W.J. Byatt, Fuzzy Differential Equations, in Proceedings of the International Conference on Cybernetics and Society, Tokyo, (1978)
1213–1216.
[6] O. Kaleva, Fuzzy Differential Equations, Fuzzy Sets and Systems, 24 (1987), 301–317.
[7] O. Kaleva, The Cauchy problem for Fuzzy Differential Equations, Fuzzy Sets and Systems, 35 (1990), 389–396.
[8] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319–330.
[9] O. He, W. Yi, On fuzzy differential Equations, Fuzzy Sets Systems, 24 (1989), 321–325.
[10] P. Kloedan, Remarks on Piano-like theorems for fuzzy differential Equations,Fuzzy Sets and Systems, 44 (1991), 161–164.
[11] S. Pederson, M. Sambandham, Numerical solution to Hybrid fuzzy systems, Mathematical and Computer Modelling, 45 (2007), 1133–1144.
[12] L. J. Jowers, J. J. Buckley K. D. Reilly, Simulating continuous fuzzy systems, Inform. Sci., 177 (2007), 436–448.
[13] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Improved Euler Method, International Journal of Applied Mathematical
Science, 38 (2012), 1847–1862.
[14] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Runge Kutta Verner Method, Far East Journal of Applied Mathematics,
86 (2014), 93–115.
[15] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Runge Kutta Method of order five, Applied Mathematical Science, 6
(2012), 69–72.
[16] K. Kanakarajan, M.Sambath, Numerical Solution for hybrid fuzzy differential equations by improved predictor-corrector method, Nonlinear Studies, 19
(2012), 171–185.
[17] M. Sambandham, Perturbed Lyapunov-like functions and Hybrid Fuzzy Differential Equations, Int. J. Hybrid Syst., 2 (2002) 23-34.
[18] C. X. Wu, M. Ma, Embedding problem of fuzzy number space Part I, Fuzzy Sets Syst.,44 (1991) 33-38.
[19] J. J.Bukley, T. Feuring, Fuzzy Differential Equations, Fuzzy Sets Syst., 110 (200) 43-54.
[1] S. L. Chang and A. Zadeh, On Fuzzy Mapping and Control, IEEEE Trans. Systems Man Cybernet 2 (1972), 30–34.
[2] D. Dubois and H.Prade, Towards Fuzzy Differential Calculus: Part 3, Differentiation, Fuzzy Sets and System, 8 (1982,) 225–233.
[3] M. L. Puri, D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983), 321–325.
[4] R. Goetschel, W.Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), 31–43.
[5] A. Kandel, W.J. Byatt, Fuzzy Differential Equations, in Proceedings of the International Conference on Cybernetics and Society, Tokyo, (1978)
1213–1216.
[6] O. Kaleva, Fuzzy Differential Equations, Fuzzy Sets and Systems, 24 (1987), 301–317.
[7] O. Kaleva, The Cauchy problem for Fuzzy Differential Equations, Fuzzy Sets and Systems, 35 (1990), 389–396.
[8] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319–330.
[9] O. He, W. Yi, On fuzzy differential Equations, Fuzzy Sets Systems, 24 (1989), 321–325.
[10] P. Kloedan, Remarks on Piano-like theorems for fuzzy differential Equations,Fuzzy Sets and Systems, 44 (1991), 161–164.
[11] S. Pederson, M. Sambandham, Numerical solution to Hybrid fuzzy systems, Mathematical and Computer Modelling, 45 (2007), 1133–1144.
[12] L. J. Jowers, J. J. Buckley K. D. Reilly, Simulating continuous fuzzy systems, Inform. Sci., 177 (2007), 436–448.
[13] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Improved Euler Method, International Journal of Applied Mathematical
Science, 38 (2012), 1847–1862.
[14] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Runge Kutta Verner Method, Far East Journal of Applied Mathematics,
86 (2014), 93–115.
[15] T. Jayakumar, K. Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Runge Kutta Method of order five, Applied Mathematical Science, 6
(2012), 69–72.
[16] K. Kanakarajan, M.Sambath, Numerical Solution for hybrid fuzzy differential equations by improved predictor-corrector method, Nonlinear Studies, 19
(2012), 171–185.
[17] M. Sambandham, Perturbed Lyapunov-like functions and Hybrid Fuzzy Differential Equations, Int. J. Hybrid Syst., 2 (2002) 23-34.
[18] C. X. Wu, M. Ma, Embedding problem of fuzzy number space Part I, Fuzzy Sets Syst.,44 (1991) 33-38.
[19] J. J.Bukley, T. Feuring, Fuzzy Differential Equations, Fuzzy Sets Syst., 110 (200) 43-54.
Thangamuthu, M., & Thippan, J. (2019). Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method. Journal of Mathematical Sciences and Modelling, 2(1), 39-50. https://doi.org/10.33187/jmsm.433538
AMA
Thangamuthu M, Thippan J. Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method. Journal of Mathematical Sciences and Modelling. April 2019;2(1):39-50. doi:10.33187/jmsm.433538
Chicago
Thangamuthu, Muthukumar, and Jayakumar Thippan. “Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method”. Journal of Mathematical Sciences and Modelling 2, no. 1 (April 2019): 39-50. https://doi.org/10.33187/jmsm.433538.
EndNote
Thangamuthu M, Thippan J (April 1, 2019) Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method. Journal of Mathematical Sciences and Modelling 2 1 39–50.
IEEE
M. Thangamuthu and J. Thippan, “Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method”, Journal of Mathematical Sciences and Modelling, vol. 2, no. 1, pp. 39–50, 2019, doi: 10.33187/jmsm.433538.
ISNAD
Thangamuthu, Muthukumar - Thippan, Jayakumar. “Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method”. Journal of Mathematical Sciences and Modelling 2/1 (April 2019), 39-50. https://doi.org/10.33187/jmsm.433538.
JAMA
Thangamuthu M, Thippan J. Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method. Journal of Mathematical Sciences and Modelling. 2019;2:39–50.
MLA
Thangamuthu, Muthukumar and Jayakumar Thippan. “Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method”. Journal of Mathematical Sciences and Modelling, vol. 2, no. 1, 2019, pp. 39-50, doi:10.33187/jmsm.433538.
Vancouver
Thangamuthu M, Thippan J. Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method. Journal of Mathematical Sciences and Modelling. 2019;2(1):39-50.