On the exact and the approximate solutions of second-order fuzzy initial value problems with constant coefficients

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DOI:

https://doi.org/10.26637/MJM0601/0009

Abstract

In this paper investigates the approximate solutions by the Adomian decomposition method and by the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear initial value problems with constant coefficients. Comparison results of the solutions is given.

Keywords:

Fuzzy initial value problem, second-order fuzzy differential equation, Hukuhara differentiability, Adomian decomposition method, the undetermined fuzzy coefficients method

Mathematics Subject Classification:

Mathematics
  • Hülya Gültekin Çitil Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun-28100, Turkey.
  • Pages: 61-68
  • Date Published: 01-01-2018
  • Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor method, Comput. Methods Appl. Math.,2 (2002), 113-124.

S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso and J. J. Nieto, Numerical methods for fuzzy differential inclusions, Journal of Computers Mathematics with Applications, 48 (2004), 1633-1641.

G. Adomian, A review of the decomposition method and some results for nonlinear equations, Math. Compute Model, 7 (1990), $17-43$

T. Allahviranloo, N. Ahmady and E. Ahmady, Numeric solutions of fuzzy differential equations by predictor-corrector method, Inf. Sci., 177 (2007), 1633-1647.

T. Allahviranloo, Nth-order fuzzy linear differential equations, Inf. Sci., 178 (2008), 1309-1324.

B. Bede and S. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equation, Fuzzy Sets Syst., 151 (2005), 581-599.

B. Bede, A Note on "Two-point boundary value problems associated with non-linear fuzzy differential equations", Fuzzy Sets and Systems, 157 (2006), 986-989.

B. Bede, Note on "Numerical solutions of fuzzy differential equations by predictor method", Inf. Sci., 178 (2008), 19171922.

J.J. Buckley and T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems, 110 (2000), 43-54.

J.J. Buckley, T. Feuring, Fuzzy initial value problem for Nthorder linear differential equation, Fuzzy Sets and Systems, 121 (2001), 247-255.

D. Dubois and H.Prade, Operations on fuzzy numbers, Int. $J$. Syst. Sci., 9 (1978), 613-626.

M. Friedman, M. Ma and A. Kandel, Numerical solution of fuzzy differential and integral equations, Fuzzy Sets and Systems, $106(1999), 35-48$.

N.A. Gasilov, S.E. Amrahov and A.G. Fatullayev, A geometric approach to solve fuzzy linear systems of differential equations, Appl. Math. Inf. Sci., 5 (2011), 484-495.

X. Guo, D. Shang and X. Lu, Fuzzy approximate solutions of second-order fuzzy linear boundary value problems, Boundary Value Problems, 2013, doi:10.1186/1687-2770-2013-212.

H. Gültekin and N. Altınışık, On solution of two-point fuzzy boundary value problems, Bulletin of Society for Mathematical Services & Standarts, 3(2) (2014), 43-53.

H. Gultekin ¨ C¸ itil and N. Altınıs¸ık, On the eigenvalues and the eigenfunctions of the Sturm-Liouville fuzzy boundary value problem, Journal of Mathematical and Computational Science, 7(4) (2017), 786-805.

E. Hüllermeir, An approach to modeling and simulation of uncertain dynamical systems, Internat. J. Uncertanity, Fuzziness, Knowledge-Based Systems, 5 (1997), 117-137.

A.Khastan and K. Ivaz, Numerical solution of fuzzy differential equations by Nyström method, Chaos Solitons Fractals, 41 (2009), 859-868.

A. Khastan and JJ. Nieto, A boundary value problem for second order fuzzy differential equations, Nonlinear Analysis, 72 (2010), 3583-3593.

H-K. Liu, Comparations results of two-point fuzzy boundary value problems, International Journal of Computational and Mathematical Sciences, 5:1 (2011).

M. L. Puri and D. A. Ralescu, Differentials for fuzzy functions, J. Math. Anal.Appl., 91 (1983), 552-558.

L. Wang and S. Guo, Adomian method for second-order fuzzy differential equation, World Academy of Science, Engineering and Technology, $76(2011), 979-982$.

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Published

01-01-2018

How to Cite

Hülya Gültekin Çitil. “On the Exact and the Approximate Solutions of Second-Order Fuzzy Initial Value Problems With Constant Coefficients”. Malaya Journal of Matematik, vol. 6, no. 01, Jan. 2018, pp. 61-68, doi:10.26637/MJM0601/0009.