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Numerical solution of fuzzy differential equations by predictor-corrector method. (English) Zbl 1183.65090

Inf. Sci. 177, No. 7, 1633-1647 (2007); erratum ibid. 178, No. 6, 1780-1782 (2008).
Summary: Three numerical methods to solve “the fuzzy ordinary differential equations” are discussed. These methods are Adams-Bashforth, Adams-Moulton and predictor-corrector. Predictor-corrector is obtained by combining Adams-Bashforth and Adams-Moulton methods. Convergence and stability of the proposed methods are also proved in detail. In addition, these methods are illustrated by solving two fuzzy Cauchy problems.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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[1] Abbasbandy, S.; Allahviranloo, T., Numerical solutions of fuzzy differential equations by Taylor method, Journal of Computational Methods in Applied Mathematics, 2, 113-124 (2002) · Zbl 1019.34061
[2] Abbasbandy, S.; Allahviranloo, T.; Lopez-Pouso, O.; Nieto, J. J., Numerical methods for fuzzy differential inclusions, Journal of Computer and Mathematics With Applications, 48, 1633-1641 (2004) · Zbl 1074.65072
[3] Abbasbandy, S.; Nieto, J. J.; Alavi, M., Tuning of reachable set in one dimensional fuzzy differential equations, Chaos, Solitons and Fractals, 26, 1337-1341 (2005) · Zbl 1073.65054
[4] Chang, S. L.; Zadeh, L. A., On fuzzy mapping and control, IEEE Transactions on Systems Man and Cybernetics, 2, 30-34 (1972) · Zbl 0305.94001
[5] Congxin, W.; Shiji, S., Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions, Information Sciences, 108, 123-134 (1998) · Zbl 0931.34041
[6] Diamond, P., Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems, 129, 65-71 (2002) · Zbl 1021.34048
[7] Dubois, D.; Prade, H., Towards fuzzy differential calculus: Part 3, differentiation, Fuzzy Sets and Systems, 8, 225-233 (1982) · Zbl 0499.28009
[8] Friedman, M.; Ma, M.; Kandel, A., Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106, 35-48 (1999) · Zbl 0931.65076
[9] Friedman, M.; Ming, M.; Kandel, A., On the validity of the Peano theorem for fuzzy differential equations, Fuzzy Sets and Systems, 86, 331-334 (1997) · Zbl 0920.34056
[10] Georgiou, D. N.; Nieto, J. J.; Rodriguez-Lopez, R., Initial value problems for higher order fuzzy differential equations, Nonlinear Analysis, 63, 587-600 (2005) · Zbl 1091.34003
[11] Isaacson, E.; Keller, H. B., Analysis of Numerical Methods (1966), Wiley: Wiley New York · Zbl 0168.13101
[12] Kaleva, O., Interpolation of fuzzy data, Fuzzy Sets and Systems, 60, 63-70 (1994) · Zbl 0827.65007
[13] Ma, M.; Friedman, M.; Kandel, A., Numerical Solutions of fuzzy differential equations, Fuzzy Sets and Systems, 105, 133-138 (1999) · Zbl 0939.65086
[14] Nieto, J. J.; Rodriguez-lopez, R., Bounded solutions for fuzzy differential and integral equations, Chaos, Solitons and Fractals, 27, 1376-1386 (2006) · Zbl 1330.34039
[15] Nieto, J. J., The Cauchy problem for continuous fuzzy differential equations, Fuzzy Sets and Systems, 102, 259-262 (1999) · Zbl 0929.34005
[16] Oregan, D.; Lakshmikantham, V.; Nieto, J. J., Initial and boundary value problems for fuzzy differential equations, Nonlinear Analysis, 54, 405-415 (2003) · Zbl 1048.34015
[17] Roman-Flores, H.; Rojas-Medar, M., Embedding of level-continuous fuzzy sets on Banach spaces, Information Sciences, 144, 227-247 (2002) · Zbl 1034.46079
[18] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987) · Zbl 0643.34005
[19] Songa, S.; Wu, C., Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 110, 55-67 (2000)
[20] Xiaoping, X.; Yongqiang, F., On the structure of solutions for fuzzy initial value problem, Fuzzy Sets and Systems, 157, 212-229 (2006) · Zbl 1093.34005
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