Improved predictor-corrector method for solving fuzzy initial value problems

In this paper, an improved predictor-corrector (IPC) method is proposed to solve the ''fuzzy initial value problem''. The IPC method is generated by combining an explicit three-step method and an implicit two-step method. The methods are compared with the methods discussed in [T. Allahviranloo, N. Ahmady, E. Ahmady, Numerical solution of fuzzy differential equations by predictor-corrector method, Information Sciences 177(7) (2007) 1633-1647], and are shown to be more accurate. The convergence and stability of the proposed methods are also presented in detail. These methods are illustrated by solving some examples.

[1]  Tofigh Allahviranloo,et al.  Numerical solution of fuzzy differential equations by predictor-corrector method , 2007, Inf. Sci..

[2]  Barnabás Bede,et al.  Note on "Numerical solutions of fuzzy differential equations by predictor-corrector method" , 2008, Inf. Sci..

[3]  Saeid Abbasbandy,et al.  NUMERICAL METHODS FOR FUZZY DIFFERENTIAL INCLUSIONS , 2004 .

[4]  Congxin Wu,et al.  Existence Theorem to the Cauchy Problem of Fuzzy Differential Equations under Compactness-Type Conditions , 1998, Inf. Sci..

[5]  Shiji Song,et al.  Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations , 2000, Fuzzy Sets Syst..

[6]  S. Seikkala.  On the fuzzy initial value problem , 1987 .

[7]  D. Dubois,et al.  Towards fuzzy differential calculus part 3: Differentiation , 1982 .

[8]  J. Nieto,et al.  Bounded solutions for fuzzy differential and integral equations , 2006 .

[9]  V LUPULESCU.  Initial value problem for fuzzy differential equations under dissipative conditions , 2008, Inf. Sci..

[10]  Rosana Rodríguez-López,et al.  Monotone method for fuzzy differential equations , 2008, Fuzzy Sets Syst..

[11]  Rosana Rodríguez-López,et al.  Periodic boundary value problems for impulsive fuzzy differential equations , 2008, Fuzzy Sets Syst..

[12]  Phil Diamond,et al.  Brief note on the variation of constants formula for fuzzy differential equations , 2002, Fuzzy Sets Syst..

[13]  Abraham Kandel,et al.  Numerical solutions of fuzzy differential and integral equations , 1999, Fuzzy Sets Syst..

[14]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[15]  Jiuping Xu,et al.  A class of linear differential dynamical systems with fuzzy initial condition , 2007, Fuzzy Sets Syst..

[16]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[17]  Tofigh Allahviranloo,et al.  Nth-order fuzzy linear differential equations , 2008, Inf. Sci..

[18]  Abraham Kandel,et al.  Numerical solutions of fuzzy differential equations , 1999, Fuzzy Sets Syst..

[19]  H Roman Flores,et al.  EMBEDDING OF LEVEL-CONTINUOUS FUZZY SETS ON BANACH SPACES , 2002 .

[20]  V. Lakshmikantham,et al.  Initial and boundary value problems for fuzzy differential equations , 2003 .

[21]  Tofigh Allahviranloo,et al.  Erratum to "Numerical solution of fuzzy differential equations by predictor-corrector method" [Inf Sci 177 (7) (2007) 1633-1647] , 2008, Inf. Sci..

[22]  Weiyin Fei,et al.  Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients , 2007, Inf. Sci..

[23]  Juan J. Nieto,et al.  Linear First-Order Fuzzy Differential Equations , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  Guoqing Liu,et al.  On fuzzy boundary value problems , 2008, Inf. Sci..

[25]  T Allahviranloo,et al.  NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATION BY TAILOR METHOD , 2002 .

[26]  Saeid Abbasbandy,et al.  Numerical methods forfuzzy differential inclusions , 2004 .

[27]  Imre J. Rudas,et al.  First order linear fuzzy differential equations under generalized differentiability , 2007, Inf. Sci..

[28]  Juan J. Nieto,et al.  The Cauchy problem for continuous fuzzy differential equations , 1999, Fuzzy Sets Syst..

[29]  Abraham Kandel,et al.  On the validity of the Peano theorem for fuzzy differential equations , 1997, Fuzzy Sets Syst..

[30]  V. Lakshmikantham,et al.  Revisiting fuzzy differential equations , 2004 .

[31]  J. Nieto,et al.  FUZZY DIFFERENTIAL SYSTEMS UNDER GENERALIZED METRIC SPACES APPROACH , 2008 .

[32]  Osmo Kaleva,et al.  A note on fuzzy differential equations , 2006 .

[33]  Yurilev Chalco-Cano,et al.  Fuzzy differential equations and the extension principle , 2007, Inf. Sci..

[34]  Heriberto Román-Flores,et al.  Embedding of level-continuous fuzzy sets on Banach spaces , 2002, Inf. Sci..

[35]  M. Murty,et al.  INITIAL AND BOUNDARY VALUE PROBLEMS FOR FUZZY DIFFERENTIAL EQUATIONS , 2007 .

[36]  Xiaoping Xue,et al.  On the structure of solutions for fuzzy initial value problem , 2006, Fuzzy Sets Syst..

[37]  Juan J. Nieto,et al.  Euler polygonal method for metric dynamical systems , 2007, Inf. Sci..

[38]  Dimitris N. Georgiou,et al.  Initial value problems for higher-order fuzzy differential equations , 2005 .

[39]  Osmo Kaleva,et al.  Interpolation of fuzzy data , 1994 .

[40]  Rosana Rodríguez-López,et al.  Comparison results for fuzzy differential equations , 2008, Inf. Sci..

[41]  Saeid Abbasbandy,et al.  Tuning of reachable set in one dimensional fuzzy differential inclusions , 2005 .