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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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##### References:
  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  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  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  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  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  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  Dubois, D.; Prade, H., Towards fuzzy differential calculus: part 3, differentiation, Fuzzy sets and systems, 8, 225-233, (1982) · Zbl 0499.28009  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  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  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  Isaacson, E.; Keller, H.B., Analysis of numerical methods, (1966), Wiley New York · Zbl 0168.13101  Kaleva, O., Interpolation of fuzzy data, Fuzzy sets and systems, 60, 63-70, (1994) · Zbl 0827.65007  Ma, M.; Friedman, M.; Kandel, A., Numerical solutions of fuzzy differential equations, Fuzzy sets and systems, 105, 133-138, (1999) · Zbl 0939.65086  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  Nieto, J.J., The Cauchy problem for continuous fuzzy differential equations, Fuzzy sets and systems, 102, 259-262, (1999) · Zbl 0929.34005  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  Roman-Flores, H.; Rojas-Medar, M., Embedding of level-continuous fuzzy sets on Banach spaces, Information sciences, 144, 227-247, (2002) · Zbl 1034.46079  Seikkala, S., On the fuzzy initial value problem, Fuzzy sets and systems, 24, 319-330, (1987) · Zbl 0643.34005  Songa, S.; Wu, C., Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy sets and systems, 110, 55-67, (2000)  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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