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Numerical solution of hybrid fuzzy differential equations using improved predictor-corrector method. (English) Zbl 1250.65092
Summary: The hybrid fuzzy differential equations have a wide range of applications in science and engineering. This paper considers numerical solutions for hybrid fuzzy differential equations. The improved predictor-corrector method is adapted and modified for solving the hybrid fuzzy differential equations. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated calculations of algorithm.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
34A07Fuzzy differential equations
68W30Symbolic computation and algebraic computation
65L06Multistep, Runge-Kutta, and extrapolation methods
Maple; Mathematica
Full Text: DOI
[1] Abbasbandy, S.; Allahviranloo, T.; Lopez-Pouso, O.; Nieto, J. J.: Numerical methods for fuzzy differential inclusions, Comput math appli 48, 1633-1641 (2004) · Zbl 1074.65072 · doi:10.1016/j.camwa.2004.03.009
[2] Allahviranloo, T.; Ahmadi, N.; Ahmadi, E.: Numerical solution of fuzzy differential equations by predictor -- corrector method, Inf sci 177, 1633-1647 (2007) · Zbl 1183.65090 · doi:10.1016/j.ins.2006.09.015
[3] Allahviranloo, T.; Kiani, N. A.; Motamedi, N.: Solving fuzzy differential equations by differential transformation method, Inf sci 179, 956-966 (2009) · Zbl 1160.65322 · doi:10.1016/j.ins.2008.11.016
[4] Allahviranloo, T.; Ahmady, E.; Ahmady, N.: Nth-order fuzzy linear differential equations, Inf sci 178, 1309-1324 (2008) · Zbl 1134.65352 · doi:10.1016/j.ins.2007.10.013
[5] Allahviranloo, T.; Abbasbandy, S.; Ahmady, E.; Ahmady, N.: Improved predictor -- corrector method for solving fuzzy initial value problems, Inf sci 179, 945-955 (2009) · Zbl 1165.65042 · doi:10.1016/j.ins.2008.11.030
[6] Barros, L. C.; Bassanezi, R. C.; Tonelli, P. A.: Fuzzy modelling in population dynamics, Ecol model 128, 27-33 (2000)
[7] Buckley, J. J.; Eslami, E.; Feuring, T.: Fuzzy mathematics in economics and engineering, (2002) · Zbl 0986.03039
[8] Friedman, M.; Ma, M.; Kandel, A.: Numerical solution of fuzzy differential and integral equations, Fuzzy sets syst 106, 35-48 (1999) · Zbl 0931.65076 · doi:10.1016/S0165-0114(98)00355-8
[9] Jafari, H.; Saeidy, M.; Vahidi, J.: The homotopy analysis method for solving fuzzy system of linear equations, Int J fuzzy syst 11, No. 4, 308-313 (2009)
[10] Kaleva, O.: Fuzzy differential equations, Fuzzy sets syst 24, 301-317 (1987) · Zbl 0646.34019 · doi:10.1016/0165-0114(87)90029-7
[11] Khastan, A.; Nieto, J. J.: A boundary value problem for second order fuzzy differential equations, Nonlinear anal TMA 72, 3583-3593 (2010) · Zbl 1193.34004 · doi:10.1016/j.na.2009.12.038
[12] Kastan, A.; Ivaz, K.: Numerical solution of fuzzy differential equations by Nyström method, Chaos, solitons fract 41, 859-868 (2009) · Zbl 1198.65113 · doi:10.1016/j.chaos.2008.04.012
[13] Pederson, S.; Sambandham, M.: Numerical solution to hybrid fuzzy systems, Math comput model 45, 1133-1144 (2007) · Zbl 1123.65069 · doi:10.1016/j.mcm.2006.09.014
[14] Pederson, S.; Sambandham, M.: Numerical solution of hybrid fuzzy differential equation ivps by a characterization theorem, Inf sci 179, 319-328 (2009) · Zbl 1165.65041 · doi:10.1016/j.ins.2008.09.023
[15] Prakash, P.; Kalaiselvi, V.: Numerical solution of hybrid fuzzy differential equations by predictor -- corrector method, Int J comput math 86, 121-134 (2009) · Zbl 1158.65049 · doi:10.1080/00207160802247620
[16] Seikkala, S.: On the fuzzy initial value problem, Fuzzy sets syst 24, 319-330 (1987) · Zbl 0643.34005 · doi:10.1016/0165-0114(87)90030-3
[17] Xu, J.; Liao, Z.; Nieto, J. J.: A class of linear differential dynamical systems with fuzzy matrices, J math anal appl 368, 54-68 (2010) · Zbl 1193.37025 · doi:10.1016/j.jmaa.2009.12.053