메뉴 건너뛰기




Volumn 15, Issue 7, 2011, Pages 1247-1253

Euler method for solving hybrid fuzzy differential equation

Author keywords

Characteristic theorem; Convergence; Euler method; Generalized Hukuhara differentiability; Hybrid fuzzy differential equations

Indexed keywords

CHARACTERISTIC THEOREM; CONVERGENCE; DIFFERENTIABILITY; EULER METHOD; FUZZY DIFFERENTIAL EQUATIONS;

EID: 79958030660     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-010-0659-y     Document Type: Article
Times cited : (42)

References (44)
  • 1
    • 85000083726 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equation by Taylor method
    • Abbasbandy S, Allahviranloo T (2002) Numerical solution of fuzzy differential equation by Taylor method. J Comput Method Appl Math 2: 113-124.
    • (2002) J Comput Method Appl Math , vol.2 , pp. 113-124
    • Abbasbandy, S.1    Allahviranloo, T.2
  • 4
    • 33846370208 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equations by predictor-corrector method
    • Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Inform Sci 177: 1633-1647.
    • (2007) Inform Sci , vol.177 , pp. 1633-1647
    • Allahviranloo, T.1    Ahmady, N.2    Ahmady, E.3
  • 5
    • 37449009203 scopus 로고    scopus 로고
    • N-th order fuzzy linear differential equations
    • Allahviranloo T, Ahmady E, Ahmady N (2008) N-th order fuzzy linear differential equations. Inform Sci 178: 1309-1324.
    • (2008) Inform Sci , vol.178 , pp. 1309-1324
    • Allahviranloo, T.1    Ahmady, E.2    Ahmady, N.3
  • 6
    • 59349083165 scopus 로고    scopus 로고
    • Toward the existence and uniqueness of solutions of second-order fuzzy differental equations
    • Allahviranloo T, Kiani NA, Barkhordari M (2009) Toward the existence and uniqueness of solutions of second-order fuzzy differental equations. Inform Sci 179: 1207-1215.
    • (2009) Inform Sci , vol.179 , pp. 1207-1215
    • Allahviranloo, T.1    Kiani, N.A.2    Barkhordari, M.3
  • 7
    • 38649113250 scopus 로고    scopus 로고
    • Note on Numerical solution of fuzzy differential equations by predictor-corrector method
    • Bede B (2008) Note on "Numerical solution of fuzzy differential equations by predictor-corrector method". Inform Sci 178: 1917-1922.
    • (2008) Inform Sci , vol.178 , pp. 1917-1922
    • Bede, B.1
  • 8
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
    • Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151: 581-599.
    • (2005) Fuzzy Sets Syst , vol.151 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 9
    • 33846224330 scopus 로고    scopus 로고
    • First order linear fuzzy differential equations under generalized differentiability
    • Bede B, Rudas IJ, Bencsik AL (2006) First order linear fuzzy differential equations under generalized differentiability. Inform Sci 177: 1648-1662.
    • (2006) Inform Sci , vol.177 , pp. 1648-1662
    • Bede, B.1    Rudas, I.J.2    Bencsik, A.L.3
  • 10
    • 0035898965 scopus 로고    scopus 로고
    • Fuzzy initial value problem for Nth-order fuzzy linear differential equations
    • Buckley JJ, Feuring T (2001) Fuzzy initial value problem for Nth-order fuzzy linear differential equations. Fuzzy Sets Syst 121: 247-255.
    • (2001) Fuzzy Sets Syst , vol.121 , pp. 247-255
    • Buckley, J.J.1    Feuring, T.2
  • 11
  • 14
    • 0032116380 scopus 로고    scopus 로고
    • Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions
    • Congxin W, Shiji S (1998) Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditins. Inform Sci 108: 123-134.
    • (1998) Inform Sci , vol.108 , pp. 123-134
    • Congxin, W.1    Shiji, S.2
  • 15
    • 0033281106 scopus 로고    scopus 로고
    • Time dependent differential inclusions, cocycle attractors and fuzzy differential equations
    • Diamond P (1999) Time dependent differential inclusions, cocycle attractors and fuzzy differential equations. IEEE Trans Fuzzy Syst 7: 734-740.
    • (1999) IEEE Trans Fuzzy Syst , vol.7 , pp. 734-740
    • Diamond, P.1
  • 16
    • 0040971094 scopus 로고    scopus 로고
    • Existence and stability of fuzzy differential equations
    • Ding Z, Kandel A (1997) Existence and stability of fuzzy differential equations. J Fuzzy Math 5(3): 681-697.
    • (1997) J Fuzzy Math , vol.5 , Issue.3 , pp. 681-697
    • Ding, Z.1    Kandel, A.2
  • 17
    • 0020184062 scopus 로고
    • Towards fuzzy differential calculus
    • Dubios D, Prade H (1982) Towards fuzzy differential calculus. Fuzzy Sets Syst 8: 225-233.
    • (1982) Fuzzy Sets Syst , vol.8 , pp. 225-233
    • Dubios, D.1    Prade, H.2
  • 18
    • 0031189750 scopus 로고    scopus 로고
    • Existence of the solutions of fuzzy differential equations with parameters
    • Ding Z, Ma M, Kandel A (1997) Existence of the solutions of fuzzy differential equations with parameters. Inform Sci 99: 205-217.
    • (1997) Inform Sci , vol.99 , pp. 205-217
    • Ding, Z.1    Ma, M.2    Kandel, A.3
  • 20
    • 0040971084 scopus 로고    scopus 로고
    • Numerical methods for calculating the fuzzy integral
    • Friedman M, Ma M, Kandel A (1996a) Numerical methods for calculating the fuzzy integral. Fuzzy Sets Syst 83: 57-62.
    • (1996) Fuzzy Sets Syst , vol.83 , pp. 57-62
    • Friedman, M.1    Ma, M.2    Kandel, A.3
  • 22
    • 0002903697 scopus 로고    scopus 로고
    • On the validity of the Peano theorem for fuzzy differential equations
    • Friedman M, Ma M, Kandel A (1997a) On the validity of the Peano theorem for fuzzy differential equations. Fuzzy Sets Syst 86: 331-334.
    • (1997) Fuzzy Sets Syst , vol.86 , pp. 331-334
    • Friedman, M.1    Ma, M.2    Kandel, A.3
  • 24
    • 0009933836 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential and integral equations
    • Friedman M, Ming M, Kandel A (1999a) Numerical solution of fuzzy differential and integral equations. Fuzzy Sets Syst 106: 35-48.
    • (1999) Fuzzy Sets Syst , vol.106 , pp. 35-48
    • Friedman, M.1    Ming, M.2    Kandel, A.3
  • 26
    • 0040812969 scopus 로고    scopus 로고
    • Solutions to fuzzy integral equations with arbitrary kernels
    • Friedman M, Ma M, Kandel A (1999c) Solutions to fuzzy integral equations with arbitrary kernels. Int J Approx Reason 20: 249-262.
    • (1999) Int J Approx Reason , vol.20 , pp. 249-262
    • Friedman, M.1    Ma, M.2    Kandel, A.3
  • 30
    • 0023573517 scopus 로고
    • Fuzzy differential equations
    • Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24: 301-317.
    • (1987) Fuzzy Sets Syst , vol.24 , pp. 301-317
    • Kaleva, O.1
  • 31
    • 0000363222 scopus 로고
    • The Cauchy problem for fuzzy differential equations
    • Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Sets Syst 35: 389-396.
    • (1990) Fuzzy Sets Syst , vol.35 , pp. 389-396
    • Kaleva, O.1
  • 32
    • 0000984385 scopus 로고
    • Remarks on Peano-like theorems for fuzzy differential equations
    • Kloeden P (1991) Remarks on peano-like theorems for fuzzy differential equations. Fuzzy Sets Syst 44: 161-164.
    • (1991) Fuzzy Sets Syst , vol.44 , pp. 161-164
    • Kloeden, P.1
  • 35
    • 33846359040 scopus 로고    scopus 로고
    • Numerical solution to hybrid fuzzy systems
    • Pederson S, Sambandham M (2007) Numerical solution to hybrid fuzzy systems. Math Comput Modell 45: 1133-1144.
    • (2007) Math Comput Modell , vol.45 , pp. 1133-1144
    • Pederson, S.1    Sambandham, M.2
  • 36
    • 40949090514 scopus 로고    scopus 로고
    • The Rungge-Kutta method for hybrid fuzzy differential equations
    • Pederson S, Sambandham M (2008) The Rungge-Kutta method for hybrid fuzzy differential equations. Nonlinear Anal Hybrid Syst 2: 626-634.
    • (2008) Nonlinear Anal Hybrid Syst , vol.2 , pp. 626-634
    • Pederson, S.1    Sambandham, M.2
  • 37
    • 55949123641 scopus 로고    scopus 로고
    • Numerical solution of hybrid fuzzy differential equation IVP by characterization theorem
    • Pederson S, Sambandham M (2009) Numerical solution of hybrid fuzzy differential equation IVP by characterization theorem. Inform Sci 179: 319-328.
    • (2009) Inform Sci , vol.179 , pp. 319-328
    • Pederson, S.1    Sambandham, M.2
  • 38
    • 0001237908 scopus 로고
    • Differential for fuzzy function
    • Puri ML, Ralescu D (1983) Differential for fuzzy function. J Math Anal Appl 91: 552-558.
    • (1983) J Math Anal Appl , vol.91 , pp. 552-558
    • Puri, M.L.1    Ralescu, D.2
  • 40
    • 33644751349 scopus 로고    scopus 로고
    • Perturbed Lyapunov-like functions and hybrid fuzzy diffrential equations
    • Sambandham M (2002) Perturbed lyapunov-like functions and hybrid fuzzy diffrential equations. Internat J Hybrid Syst 2: 23-34.
    • (2002) Internat J Hybrid Syst , vol.2 , pp. 23-34
    • Sambandham, M.1
  • 41
    • 0023581045 scopus 로고
    • On the fuzzy initial value problem
    • Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24: 319-330.
    • (1987) Fuzzy Sets Syst , vol.24 , pp. 319-330
    • Seikkala, S.1
  • 42
    • 67349163185 scopus 로고    scopus 로고
    • Generalized Hukuhara differentiability of interval-valued functions and interval differential equations
    • Stefanini L, Bede B (2010) Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal Theory Methods Appl 71: 1311-1328.
    • (2010) Nonlinear Anal Theory Methods Appl , vol.71 , pp. 1311-1328
    • Stefanini, L.1    Bede, B.2
  • 43
    • 34548156679 scopus 로고    scopus 로고
    • A class of linear differential dynamical systems with fuzzy initial condition
    • Xu J, Liao Z, Hu Z (2007) A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Sets Syst 158: 2339-2358.
    • (2007) Fuzzy Sets Syst , vol.158 , pp. 2339-2358
    • Xu, J.1    Liao, Z.2    Hu, Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.