Modified k-step method for solving fuzzy initial value problems

Iranian Journal of Fuzzy Systems

Volumn 8, Issue 1, 2011, Pages 49-63

  Fard, O Solaymani ^a   Kamyad, A Vahidian ^b  

^a DAMGHAN UNIVERSITY   (Iran)

^b FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

Author keywords

Fuzzy differential equations; Fuzzy numbers; Modified k step method

Indexed keywords

EID: 79955026678     PISSN: 17350654     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos, Solitons Fractals, 26 (2005), 1337-1341.
2. S. Abbasbandy, T. Allahviranloo, O. Lpez-Pouso and J. J. Nieto, Numerical methods for fuzzy differential inclusions, Comput. Math. Appl., 48 (2004), 1633-1641.
3. S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor method, Journal of Computational Methods in Applied Mathematics, 2 (2002), 113-124.
4. T. Allahviranloo, N. Ahmady and E. Ahmady, Numerical solution of fuzzy differential equa- tions by predictor-corrector method, Information Sciences, 177 (2007), 1633-1647.
5. T. Allahviranloo, N. Ahmady and E. Ahmady, Improved predictorcorrector method for solving fuzzy initial value problems, Information Sciences, 179 (2009), 945-955.
6. B. Bede, Note on Numerical solutions of fuzzy differential equations by predictor-corrector method, Information Sciences, 178 (2008), 1917-1922.
7. B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy umber valued functions with applications to fuzzy differential equation, Fuzzy Sets and Systems, 151 (2005), 581-599.
8. B. Bede, J. Imre, C. Rudas and L. Attila, First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177 (2007), 3627-3635.
9. J. J. Buckley and T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems, 110 (2000),43-54.
10. Y. Chalco-Cano and H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals, 38 (2008), 112-119.
11. Y. Chalco-Cano, H. Roman-Flores, M. A. Rojas-Medar, O. Saavedra and M. Jimnez-Gamero, The extension principle and a decomposition of fuzzy sets, Information Sciences, 177 (2007), 5394-5403.
12. C. K. Chen and S. H. Ho, Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and Computation, 106 (1999), 171-179.
13. Y. J. Cho and H. Y. Lan, The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions, Dynamics Continuous Discrete Inpulsive Systems Ser. AMath. Anal., 14 (2007), 873-884.
14. W. Congxin and S. Shiji, Exitance theorem to the Cauchy problem of fuzzy differential equa- tions under compactance-type conditions, Information Sciences, 108 (1993), 123-134.
15. P. Diamond, Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations, IEEE Trans. Fuzzy Systems, 7 (1999), 734-740.
16. P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems, 129 (2002), 65-71.
17. Z. Ding, M. Ma and A. Kandel, Existence of solutions of fuzzy differential equations with parameters, Information Sciences, 99 (1997), 205-217.
18. D. Dubois and H. Prade, Towards fuzzy differential calculus: part 3, differentiation, Fuzzy Sets and Systems, 8 (1982), 225-233.
19. W. Fei, Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients, Information Sciences, 177 (2007), 329-4337.
20. R. Goetschel and W. Voxman, Topological properties of fuzzy number, Fuzzy Sets and Sys- tems, 10 (1983), 87-99.
21. R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy sets and Systems, 18 (1986), 31-43.
22. M. S. Hashemi, M. K. Mirnia and S. Shahmorad, Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an M-matrix, Iranian Journal of Fuzzy Systems, 5(3)(2008),15-30.
23. H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, A note on evaluation of fuzzy linear regression models by comparing membership functions, Iranian Journal of Fuzzy Systems, 6(2)(2009),1-8.
24. P. Henrici, Discrete vatiablr methods in ordinary differential equations, Wiley, New York, 1962.
25. M. J. Jang, C. L. Chen and Y. C. Liy, On solving the initial-value problems using the differ- ential transformation method, Applied Mathematics and Computation, 115 (2000), 145-160.
26. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
27. O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35 (1990),389-396.
28. O. Kaleva, A note on fuzzy differential equations, Nonlinear Analysis, 64 (2006), 895-900.
29. V. Lakshmikantham and S. Leela, Differential and integral inequalities, Academic Press, New York, 1 (1969).
30. R. R. Lopez, Comparison results for fuzzy differential equations, Information Sciences, 178 (2008),1756-1779.
31. M. Ma, M. Friedman and A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems, 105 (1999) 133-138.
32. M. Ma, M. Friedman and A. Kandel, A new approach for defuzzification, Fuzzy Sets and Systems, 111 (2000), 351-356.
33. D. ÓRegan, V. Lakshmikantham and J. Nieto, Initial and boundary value problems for fuzzy differential equations, Nonlinear Anal., 54 (2003), 405-415.
34. M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Roman-Flores and R. C. Bassanezi, Fuzzy differential equations and the extension principle, Information Sciences, 177 (2007), 3627-3635.
35. S. C. Palligkinis, G. Stefanidou and P. Efraimidi, Runge-Kutta methods for fuzzy differential equations, Applied Mathematics and Computation, 209 (2009), 97-105.
36. G. Papaschinopoulos, G. Stefanidou and P. Efraimidi, Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument, Information Sciences, 177 (2007), 3855-3870.
37. M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91 (1983), 552-558.
38. R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for -weakly commuting maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 47-54.
39. M. R. Safi, H. R. Maleki and E. Zaeimazad, A note on Zimmermann method for solving fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-46.
40. S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319-330.
41. A. K. Shaymal and M. Pal, Triangular fuzzy matrices, Iranian Journal of Fuzzy Systems, 4(1) (2007),75-87.
42. S. Song, L. Guo and C. Feng, Global existence of solutions to fuzzy differential equations, Fuzzy Sets and Systems, 115 (2000), 371-376.