Volume 9 | Number 1 | Year 2014 | Article Id. IJMTT-V9P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P507
In this paper we study numerical methods for hybrid fuzzy differential equations by an application of the Adams fifth order predictor-corrector method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
[1] S.Abbasbandy, T.Allah Viranloo, Numerical solution of fuzzy differential equation by Taylor method, Journal of Computational Methods in Applied mathematics, 2 (2002) 113-124.
[2] S.Abbasbandy, T.Allah Viranloo, Numerical solution of fuzzy differential equation, Mathematical and Computational Applications, 7 (2002) 41-52.
[3] S.Abbasbandy, T.Allah Viranloo, Numerical solution of fuzzy differential equation by Runge- Kutta method, Nonlinear Studies, 11 (2004) 117-129.
[4] B.Bede, Note on Numerical solutions of fuzzy differential equations by predictor corrector method, Information science 178 (2008) 1917-1922.
[5] J.J.Bukley, T.Feuring, Fuzzy Differential Equations, Fuzzy Sets and Systems, 110 (2000) 43- 54.
[6] R.Goetschel, Woxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986) 31-43.
[7] T.Jayakumar, K.Kanakarajan, Numerical Solution for Hybrid Fuzzy System by Improved Euler Method, International Journal of Applied Mathematical Science, 38 (2012) 1847-1862.
[8] T.Jayakumar, K.Kanakarajan, S.Indrakumar, Numerical Solution of Nth- Order Fuzzy Differential equation by Runge-Kutta Nystrom method, International Journal of Mathematical Engineering and Science, 1(5) 2012 1-13.
[9] T.Jayakumar, D.Maheshkumar, K.Kanagarajan, Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method of Order Five, International Journal of Applied Mathematical Science, 6 (2012) 2989-3002.
[10] T.Jayakumar, K.Kanagarajan, Numerical Solution for Hybrid Fuzzy System by Runge-Kutta Method of Order Five, International Journal of Applied Mathematical Science, 6 (2012) 3591- 3606.
[11] M.K.Jain, S.R.K. Iyanger, and R.K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publishers, New Delhi, 2005.
[12] O.Kaleva, Interpolation of fuzzy data, Fuzzy Sets and Systems, 60 (1994), 63-70.
[13] O.Kaleva, Fuzzy Differential Equations, Fuzzy Sets and Systems, 24 (1987) 301-317.
[14] K.Kanagarajan, M.Sambath Numerical Solution for Fuzzy Differential Equations by Third Order Runge-Kutta Method, International Journal of Applied Mathematics and Computation, 2(4) (2010) 1-10.
[15] K.Kanagarajan, M.Sambath Numerical Solution for Fuzzy Differential Equations by improved predictor-corrector method, 19, 2(2012), Non linear studies.
[16] V.Lakshmikantham, X.Z.Liu, Impulsive Hybrid systems and stability theory, International Journal of Nonlinear Differential Equations, 5 (1999) 9-17.
[17] V.Lakshmikantham, R.N.Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, United Kingdom, 2003.
[18] M.Ma, M.Friedman, A.Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems, 105 (1999) 133-138.
[19] S.Pederson, M.Sambandham, Numerical solution to Hybrid fuzzy systems, Mathematical and Computer Modelling, 45(2007) 1133-1144.
[20] S.Pederson, M.Sambandham, The Runge-Kutta method for Hybrid Fuzzy Differential Equations, Nonlinear Analysis Hybrid Systems, 2 (2008) 626-634.
[21] P.Prakash, V.Kalaiselvi, Numerical solution of Hybrid Fuzzy Differential Equations by predictor-corrector method, International Journal of Computer Mathematics, 86 (2009), 121- 134
[22] M.Sambandham, Perturbed Lyapunov-like functions and Hybrid Fuzzy Differential Equations, International Journal of Hybrid Systems, 2 (2002) 23-34.
[23] S.Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987) 319-330.
T. Jayakumar , K. Kanagarajan, "Numerical Solution of Hybrid Fuzzy Differential Equations by Adams Fifth Order Predictor-Corrector Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 1, pp. 70-83, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P507