Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations

Using a fixed point technique, the sequence of successive approximations and a recent quadrature formula for fuzzy-number-valued functions, it is constructed a numerical method for the solution of nonlinear fuzzy Fredholm integral equations. Moreover, the error estimate of the method and a criterion to stop the corresponding algorithm are given.

[1]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[2]  Jong Yeoul Park,et al.  On the existence and uniqueness of solutions of fuzzy Volterra-Fredholm integral equations , 2000, Fuzzy Sets Syst..

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

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

[5]  Luciano Stefanini,et al.  Parametric representation of fuzzy numbers and application to fuzzy calculus , 2006, Fuzzy Sets Syst..

[6]  Eyke Hüllermeier,et al.  Numerical Methods for Fuzzy Initial Value Problems , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  John N. Mordeson,et al.  Fuzzy Integral Equations , 1995, Inf. Sci..

[8]  Saeid Abbasbandy,et al.  Numerical Solution of Fuzzy Differential Equation by Runge-Kutta Method , 2004 .

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

[10]  George A. Anastassiou.  A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE , 2010 .

[11]  Alexandru Mihai Bica,et al.  TRAPEZOIDAL INEQUALITY FOR LIPSCHITZIAN VECTOR-VALUED FUNCTIONS AND AN APPLICATION , 2007 .

[12]  G. Anastassiou.  Handbook of Analytic Computational Methods in Applied Mathematics , 2000 .

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

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

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

[16]  Jong Yeoul Park,et al.  The approximate solutions of fuzzy functional integral equations , 2000, Fuzzy Sets Syst..

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

[18]  Osmo Kaleva.  The Cauchy problem for fuzzy differential equations , 1990 .

[19]  V. Lakshmikantham,et al.  TWO-POINT BOUNDARY VALUE PROBLEMS ASSOCIATED WITH NON-LINEAR FUZZY DIFFERENTIAL EQUATIONS , 2001 .

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

[21]  Young Chel Kwun,et al.  Existence of solutions of fuzzy integral equations in Banach spaces , 1995 .

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

[23]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[25]  D N Georgiou,et al.  ON FUZZY FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS , 2001 .

[26]  V. Lakshmikantham,et al.  Theory of Fuzzy Differential Equations and Inclusions , 2003 .

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

[28]  Congxin Wu,et al.  On Henstock integral of fuzzy-number-valued functions (I) , 2001, Fuzzy Sets Syst..

[29]  K Balachandran,et al.  EXISTENCE OF SOLUTIONS OF NONLINEAR FUZZY INTEGRAL EQUATIONS IN BANACH SPACES , 2001 .

[30]  Jong Yeoul Park,et al.  A note on fuzzy integral equations , 1999, Fuzzy Sets Syst..

[31]  H. Román-Flores,et al.  On new solutions of fuzzy differential equations , 2008 .

[32]  Dimitris N. Georgiou,et al.  BOUNDED SOLUTIONS FOR FUZZY INTEGRAL EQUATIONS , 2002 .

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

[34]  Abraham Kandel,et al.  Solutions to fuzzy integral equations with arbitrary kernels , 1999, Int. J. Approx. Reason..

[35]  S C Arora,et al.  SOLUTION OF INTEGRAL EQUATIONS IN FUZZY SPACES , 1998 .

[36]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

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

[38]  Barnabás Bede,et al.  A note on "two-point boundary value problems associated with non-linear fuzzy differential equations" , 2006, Fuzzy Sets Syst..

[39]  Osmo Kaleva.  Fuzzy differential equations , 1987 .

[40]  Abraham Kandel,et al.  On Fuzzy Integral Equations , 1999, Fundam. Informaticae.

[41]  Yuhu Feng.  Fuzzy-valued mappings with finite variation, fuzzy-valued measures and fuzzy-valued Lebesgue-Stieltjes integrals , 2001, Fuzzy Sets Syst..

[42]  Tofigh Allahviranloo,et al.  The Adomian Decomposition Method Applied to the Fuzzy System of Fredholm Integral Equations of the Second Kind , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[43]  Barnabás Bede,et al.  Quadrature rules for integrals of fuzzy-number-valued functions , 2004, Fuzzy Sets Syst..

[44]  Krishnan Balachandran,et al.  Existence of solutions of general nonlinear fuzzy Volterra-Fredholm integral equations , 2005 .

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

[46]  Congxin Wu,et al.  Embedding problem of noncompact fuzzy number space E∼ (I) , 1999, Fuzzy Sets Syst..

[47]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..

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

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

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

[51]  Esmail Babolian,et al.  Numerically solution of fuzzy differential equations by Adomian method , 2004, Appl. Math. Comput..

[52]  Sorin G. Gal.  Approximation Theory in Fuzzy Setting , 2000 .