Volume 16 | Number 2 | Year 2014 | Article Id. IJMTT-V16P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V16P512
In this paper numerical solution of second order linear fuzzy differential equations [15] using Leapfrog method is considered. The obtained discrete solutions using Leapfrog method are compared with the exact solutions of the second order fuzzy differential equations and single-term Haar wavelet series (STHWS) method [15]. Tables and graphs are presented to show the efficiency of this method. This Leapfrog method can be easily implemented in a digital computer and the solution can be obtained for any length of time.
[1] S. Abbasbandy and T. Allahviranloo, “Numerical solutions of fuzzy differential equations by Taylor method”, Journal of Computational Methods in Applied Mathematics. vol.2, pp. 113-124, 2002.
[2] T. Allahviranloo, N. Ahmady, and E. Ahmady, “Numerical solution of fuzzy differential equations by predictor-corrector method”, Information Sciences, vol. 177, no. 7, pp. 1633–1647, 2007.
[3] J.J. Buckley and T. Feurihg, “Fuzzy Differential Equations”, Fuzzy Sets and Systems, vol.110, pp.43-54, 2000.
[4] S. S. L. Chang andL. A. Zadeh, “On fuzzy mapping and control”, IEEE Transactions on Systems, Man, and Cybernetics, vol. 2, pp.30–34, 1972.
[5] D. Dubois and H. Prade, “Towards fuzzy differential calculus.III. Differentiation”, Fuzzy Sets and Systems, vol. 8, no. 3, pp.225–233, 1982.
[6] E. Hllermeier, Numerical methods for fuzzy initial value problems, International Journal of Uncertainty Fuzziness Knowledge-Based Systems, 7 (1999) 439-461.
[7] O. Kaleva, “Fuzzy differential equations”, Fuzzy Sets and Systems, vol. 24, no. 3, pp. 301–317, 1987.
[8] O. Kaleva, “The Cauchy problem for fuzzy differential equations”, Fuzzy Sets and Systems, vol. 35, no. 3, pp. 389–396, 1990.
[9] A. Kandel, W. J. Byatt, Fuzzy differential equations, in: Proceedings of International Conference Cybernetics and Society, Tokyo: (1978) 1213-1216.
[10] S. Karunanithi, S. Chakravarthy and S. Sekar, “Comparison of Leapfrog and single term Haar wavelet series method to solve the second order linear system with singular-A”, Journal of Mathematical and Computational Sciences (JMCS), Vol. 4, No. 4, 2014, pp. 804-816.
[11] M. L. Puri and D. A. Ralescu, “Differentials of fuzzy functions”, Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 552–558, 1983.
[12] F. Rabiei, F. Ismail, Ali Ahmadian, and Soheil Salahshour, “Numerical Solution of Second-Order Fuzzy Differential Equation Using Improved Runge-Kutta Nystrom Method”, Mathematical Problems in Engineering, 1-10, 2013.
[13] S. Seikkala, “On the fuzzy initial value problem,” Fuzzy Sets and Systems, vol. 24, no. 3, pp. 319–330, 1987.
[14] S. Sekar and K. Prabhavathi, “Numerical solution of first order linear fuzzy differential equations using Leapfrog method”, IOSR Journal of Mathematics (IOSR-JM), vol. 10, no. 5, ver. I, pp. 07-12, 2014.
[15] S. Sekar and S. Senthilkumar, “A Study on Second-Order Fuzzy Differential Equations using STHWS Method”, International Journal of Scientific & Engineering Research (IJSER), vol. 5, no. 1, pp. 2111-2114, 2014.
[16] S. Sekar and M. Vijayarakavan, “Numerical Investigation of first order linear Singular Systems using Leapfrog Method”, International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 2, pp. 89-93, 2014.
S. Sekar, K. Prabhavathi, "Numerical Solution of Second Order Fuzzy Differential Equations by Leapfrog Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 16, no. 2, pp. 74-78, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V16P512