Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients

Information Sciences

Volumn 181, Issue 20, 2011, Pages 4765-4779

  Fard, Omid Solaymani ^a   Ghal Eh, Nima ^a  

^a DAMGHAN UNIVERSITY   (Iran)

Author keywords

Approximate analytical solution; System of first order linear FDEs; Variational iteration method

Indexed keywords

APPROXIMATE-ANALYTICAL SOLUTION; CONSTANT COEFFICIENTS; EIGEN-VALUE; EXACT SOLUTION; FIRST-ORDER; FUZZY DIFFERENTIAL EQUATIONS; NUMERICAL EXPERIMENTS; NUMERICAL SOLUTION; VARIATIONAL ITERATION METHOD;

DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; LINEAR SYSTEMS; NUMERICAL METHODS;

DIFFERENTIATION (CALCULUS);

EID: 79960565924     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2011.06.007     Document Type: Article

References (58)

1. S. Abbasbandy, and T. Allahviranloo Numerical solutions of fuzzy differential equations by Taylor method J. Comput. Meth. Appl. Math. 2 2002 113 124
2. S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso, and J.J. Nieto Numerical methods for fuzzy differential inclusions Comput. Math. Appl. 48 2004 1633 1641 (Pubitemid 40608826)
3. S. Abbasbandy, J.J. Nieto, and M. Alavi Tuning of reachable set in one dimensional fuzzy differential inclusions Chaos Soliton. Fractals 26 2005 1337 1341 (Pubitemid 40821860)
4. T. Allahviranloo, N. Ahmady, and E. Ahmady Numerical solution of fuzzy differential equations by predictor-corrector method Inform. Sci. 177 2007 1633 1647 (Pubitemid 46127485)
5. S. Bandyopadhyay An efficient technique for superfamily classification of amino acid sequences: feature extraction, fuzzy clustering and prototype selection Fuzzy Set. Syst. 152 2005 5 16 (Pubitemid 40391248)
6. S. Barro, and R. Marn Fuzzy Logic in Medicine 2002 Physica-Verlag Heidelberg
7. B. Bede Note on "Numerical solutions of fuzzy differential equations by predictor-corrector method" Inform. Sci. 178 2008 1917 1922
8. B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation Fuzzy Set. Syst. 151 2005 581 599 (Pubitemid 40305079)
9. B. Bede, J. Imre, C. Rudas, and L. Attila First order linear fuzzy differential equations under generalized differentiability Inform. Sci. 177 2007 3627 3635
10. J.J. Buckley, and T. Feuring Fuzzy differential equations Fuzzy Set. Syst. 110 2000 43 54
11. J.J. Buckley, T. Feuring, and Y. Hayashi Linear systems of first order ordinary differential equations: fuzzy initial conditions Soft Comput. 6 2002 415 421
12. J.J. Buckley, and L.J. Jowers Simulating Continuous Fuzzy Systems 2006 Springer-Verlag Berlin Heidelberg
13. J. Casasnovas, and F. Rossell Averaging fuzzy biopolymers Fuzzy Set. Syst. 152 2005 139 158 (Pubitemid 40391256)
14. Y. Chalco-Cano, and H. Román-Flores On new solutions of fuzzy differential equations Chaos Soliton. Fractals 2006 1016 1043
15. Y. Chalco-Cano, Román-Flores, M.A. Rojas-Medar, O. Saavedra, and M. Jimnez-Gamero The extension principle and a decomposition of fuzzy sets Inform. Sci. 177 2007 5394 5403 (Pubitemid 47422256)
16. B.C. Chang, and S.K. Halgamuge Protein motif extraction with neuro-fuzzy optimization Bioinformatics 18 2002 1084 1090 (Pubitemid 34919229)
17. C.K. Chen, and S.H. Ho Solving partial differential equations by two-dimensional differential transform method Appl. Math. Comput. 106 1999 171 179
18. Y.J. Cho, and H.Y. Lan The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions Dyn. Contin. Discrete Impulsive Syst. Ser. A Math. Anal. 14 2007 873 884
19. W. Congxin, and S. Shiji Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions Inform. Sci. 108 1993 123 134 (Pubitemid 128383832)
20. P. Diamond Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations IEEE Trans. Fuzzy Syst. 7 1999 734 740 (Pubitemid 32212164)
21. P. Diamond Brief note on the variation of constants formula for fuzzy differential equations Fuzzy Set. Syst. 129 2002 65 71 (Pubitemid 34544383)
22. Z. Ding, M. Ma, and A. Kandel Existence of solutions of fuzzy differential equations with parameters Inform. Sci. 99 1997 205 217
23. D. Dubois, and H. Prade Towards fuzzy differential calculus: Part 3, differentiation Fuzzy Set. Syst. 8 1982 225 233 (Pubitemid 14449675)
24. M.S. El Naschie On a fuzzy Khler manifold which is consistent with the two slit experiment Int. J. Nonlinear Sci. Numer. Simult. 6 2005 95 98 (Pubitemid 40588615)
25. O.S. Fard, Z. Hadi, N. Ghal-Eh, and A.H. Borzabadi A note on iterative method for solving fuzzy initial value problems J. Adv. Res. Sci. Comput. 1 1 2009 22 33
26. O.S. Fard A numerical scheme for fuzzy cauchy problems J. Uncertain Syst. 3 4 2009 307 314
27. O.S. Fard An iterative scheme for the solution of generalized system of linear fuzzy differential equations World Appl. Sci. J. 7 12 2009 1597 1604
28. O.S. Fard, and A.V. Kamyad Modified k-step method for solving fuzzy initial value problems Iran. J. Fuzzy Syst. 8 3 2011 49 63
29. O.S. Fard, T.A. Bidgoli, and A.H. Borzabadi Approximate-analytical approach to nonlinear FDEs under generalized differentiability J. Adv. Res. Dyn. Control Syst. 2 2010 56 74
30. W. Fei Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients Inform. Sci. 177 2007 329 4337
31. R. Goetschel, and W. Voxman Elementary fuzzy calculus Fuzzy Set. Syst. 18 1986 31 43
32. J.H. He A new approach to nonlinear partial differential equations Commun. Nonlinear Sci. Numer. Simul. 2 4 1997 230 235
33. J.H. He Approximate solution of nonlinear differential equations with convolution product nonlinearites Comput. Methods Appl. Mech. Eng. 167 1998 69 73
34. J.H. He A coupling method of a homotopy technique and a perturbation technique for non-linear problems Int. J. Nonlinear Mech. 35 2000 37 43
35. J.H. He Homotopy perturbation method: a new nonlinear analytical technique Appl. Math. Comput. 135 2003 73 79
36. J.H. He Application of homotopy perturbation method to nonlinear wave equations Chaos Soliton. Fractals 26 2005 695 700
37. M.J. Jang, C.L. Chen, and Y.C. Liy On solving the initial-value problems using the differential transformation method Appl. Math. Comput. 115 2000 145 160
38. L.J. Jowers, J.J. Buckley, and K.D. Reilly Simulating continuous fuzzy systems Inform. Sci. 177 2007 436 448 (Pubitemid 44634444)
39. O. Kaleva Fuzzy differential equations Fuzzy Set. Syst. 24 1987 301 317
40. O. Kaleva The Cauchy problem for fuzzy differential equations Fuzzy Set. Syst. 35 1990 389 396
41. O. Kaleva A note on fuzzy differential equations Nonlinear Anal. 64 2006 895 900 (Pubitemid 43052526)
42. K.S. Krane Introductory Nuclear Physics 1988 John Wiley and Sons
43. V. Lakshmikantham, and S. Leela Differential and Integral Inequalities vol. 1 1969 Academic Press New York
44. R.R. Lopez Comparison results for fuzzy differential equations Inform. Sci. 178 2008 1756 1779
45. M. Ma, M. Friedman, and A. Kandel Numerical solutions of fuzzy differential equations Fuzzy Set. Syst. 105 1999 133 138 (Pubitemid 129523994)
46. C.D. Meyer Matrix Analysis and Applied Linear Algebra 2004 SIAM
47. M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Román-Flores, and R.C. Bassanezi Fuzzy differential equations and the extension principle Inform. Sci. 177 2007 3627 3635 (Pubitemid 46920529)
48. M. Oberguggenberger, and S. Pittschmann Differential equations with fuzzy parameters Math. Mod. Syst. 5 1999 181 202
49. M. Olinick An Introduction to Mathematical Model in the Social and Life Sciences 1978 Addision-Wesley Reading, MA
50. G. Papaschinopoulos, G. Stefanidou, and P. Efraimidi Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument Inform. Sci. 177 2007 3855 3870 (Pubitemid 46961976)
51. W. Pedrycz, and F. Gomide An Introduction to Fuzzy Sets: Analysis and Design (Complex Adaptive Systems) 1998 The MIT Press
52. W. Pedrycz, and F. Gomide Fuzzy Systems Engineering Toward Human-Centric Computing 2007 Wiley-IEEE Press
53. M.L. Puri, and D.A. Ralescu Differentials of fuzzy functions J. Math. Anal. Appl. 91 1983 552 558
54. H. Román-Flores, and Y. Chalco-Cano Robinsons chaos in set-valued discrete systems Chaos Soliton. Fract. 25 2005 33 42 (Pubitemid 40220059)
55. H. Román-Flores, and Y. Chalco-Cano Some chaotic properties of Zadehs extension Chaos Soliton. Fract. 35 2008 112 119
56. D.K. Salkuyeh Convergence of the variational iteration method for solving linear systems of ODEs with constant coefficients Comput. Math Appl. 56 2008 2027 2033
57. S. Seikkala On the fuzzy initial value problem Fuzzy Set. Syst. 24 1987 319 330
58. S. Song, L. Guo, and C. Feng Global existence of solutions to fuzzy differential equations Fuzzy Set. Syst. 115 2000 371 376