Keywords:-

Keywords: Fuzzy initial value problem, Dependency problem in fuzzy computation, Adams-Bashforth, Adams-Moulton, predictor-corrector methods.

Article Content:-

Abstract

In this paper, we study the numerical solution of Fuzzy Differential Equations by using predictor-corrector method which is obtained by combining Adams-Bashforth three-step method and Adams-Moulton two-step method. This method is adopted to solve the dependency problem in fuzzy computation. In addition, these methods are illustrated by solving two fuzzy cauchy problems.

References:-

References

S. Abbasbandy, T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor

Method, Computational Methods in Applied Mathematics, 2 (2002), 113-124.

S. Abbasbandy, T. Allahviranloo, Numerical solution of Fuzzy differential equation by Runge-

Kutta method, Nonlinear Studies, 11, (2004), 117-129.

M. Ahamad, M. Hasen, A new approach to incorporate uncertainity into Euler method, Applied

Mathematical Sciences , 4(51), (2010), 2509-2520.

M. Ahamed, M. Hasan, A new fuzzy version of Euler's method for solving diffrential equations

with fuzzy initial values, Sians Malaysiana, 40, (2011), 651-657.

M. Ahmad, M. Hasan, Incorporating optimization technique into Zadeh's extension principle for

computing non-monotone functions with fuzzy variable, Sains Malaysiana, 40, (2011) 643-650.

N. Z. Ahmad, H. K. Hasan, B. De Baets, A new method for computing continuous function

with fuzzy variable, Journal of Applied Sciences, 11(7) ,(2011), 1143-1149.

A. H. Alsonosi Omar, Y. Abu Hasan, Numerical solution of fuzzy differential equations and

the dependency problem, Applied Mathematics and Computation, 219, (2012), 1263-1272.

T. Allahviranloo, N. Ahmady, E. Ahmady, Numerical solutions of fuzzy differential equations

by predictor-corrector method, Information Sciences 177(7) (2007) 1633-1647.

T. Allahviranloo, N. Ahmady, E. Ahmady, Erratum to ``Numerical solutions of fuzzy

differential equations by predictor-corrector method, Inform. Sci. 177(7) (2007) 1633-1647]",

Information Sciences 178 (2008) 1780-1782.

Barnabas Bede, Note on ``Numerical solutions of fuzzy differential equations by predictorcorrector

method", Information Sciences 178 (2008) 1917-1922.

A. Bonarini, G. Bontempi, A Qualitative simulation approach for fuzzy dynamical models,

ACM Trans. Model. Comput. Simulat, 4, (1994), 285-313.

R. Brent, Algorithms for Minimization without Derivatives, Dover Pubns, 2002.

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

D. Dubois, H. Prade, Towards fuzzy differential calculus part 3: differentiation, Fuzzy Sets and

Systems, 8, (1982), 225-233.

E. Isaacson, H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966.

Kaleva Osmo, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.

O. Kaleva, Interpolation of fuzzy data, Fuzzy Sets and Systems 60(1994) 63-70.

M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy

Sets and Systems 105 (1999) 133-138.

R. E. Moore, Interval Analysis, Parentice-Hall, Englewood cliffs, N.J 1966.

S. Palligkinis, G. Papageorgiou, I. Famelis, Runge-Kutta methods for fuzzy differential

equations, Applied Mathematics and Computation 209 (2009) 97-105.

S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24(3) (1987) 319-330.

L. A. Zadeh, Fuzzy Sets, Information and Control 8(1965) 338-353.

Downloads

Citation Tools

How to Cite
Kanagarajan, K., Indrakumar, S., & Muthukumar, S. (2014). Numerical solution of fuzzy differential equations by Adams predictor-corrector method and the dependency problem. International Journal Of Mathematics And Computer Research, 2(07), 531-540. Retrieved from http://ijmcr.in/index.php/ijmcr/article/view/159