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Numerical Solution for Hybrid Fuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom Method

Year 2019, , 39 - 50, 20.04.2019
https://doi.org/10.33187/jmsm.433538

Abstract

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.

References

  • [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.
Year 2019, , 39 - 50, 20.04.2019
https://doi.org/10.33187/jmsm.433538

Abstract

References

  • [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.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Muthukumar Thangamuthu

Jayakumar Thippan This is me

Publication Date April 20, 2019
Submission Date June 13, 2018
Acceptance Date January 22, 2019
Published in Issue Year 2019

Cite

APA 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.

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