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Year 2015, Volume: 3 Issue: 1, 137 - 153, 15.05.2015

Mine Aylin Bayrak Emine Can

https://doi.org/10.36753/mathenot.421232

Abstract

References

  • [1] Guo, M., Xue, X. and Li, R., Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets and Systems 138 (2003), 601-615.
  • [2] El Naschie, M.S., A review of E-infinite theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 19 (2004), 209-236.
  • [3] El Naschie, M.S., The concepts of E-infinite: an elementary introduction to the Cantorianfractal theory of quantum physics. Chaos, Solitons and Fractals 22 (2004), 495-511.
  • [4] El Naschie, M.S., On a fuzzy Khler manifold which is consistent with the two slit experiment. International Journal of Nonlinear Science Numerical Simulation 6 (2005), 95-98.
  • [5] Tanaka,Y., Mizuna Y. and Kado, T., Chaotic dynamics in the Friedman equation. Chaos, Solitons and Fractals 24 (2005), 407-422.
  • [6] El Naschie, M.S., From experimental quantum optics to quantum gravity via a fuzzy Khler manifold. Chaos, Solitons and Fractals 25 (2005), 969-977.
  • [7] Zhang, H., Liao, X. and Yu, J., Fuzzy modelling and synchronization of hyperchaotic systems. Chaos, Solitons and Fractals 26 (2005), 835-843.
  • [8] Feng, G. and Chen, G., Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos, Solitons and Fractals 23 (2005), 459-467.
  • [9] Jiang, W., Guo-Dang, Q. and Bin, D., H∞ variable universe adaptive fuzzy control for chaotic systems. Chaos, Solitons and Fractals 24 (2005), 1075-1086.
  • [10] Abbad, M.F.,Von Keyserlingk, D.G.,Linkens, D.A. and Mahfouf,M., Survey of utilisation of fuzzy technology in medicine and healthcare. Fuzzy Sets and Systems 120 (2001), 331-349.
  • [11] Barro, S. and Marn, R.,Fuzzy logic in medicine,Heidelberg, Physica-verlag,2002.
  • [12] Helgason, C.M. and Jobe, T.H., The fuzzy cube and causal efficiacy: representation of concomitant mechanisms in stroke. Neural Networks 11 (1998), 549-555.
  • [13] Nieto, J.J. and Torres, A., Midpoints for fuzzy sets and their application in medicine. Artificial Intelligence in Medicine 27 (2003), 81-101.
  • [14] Bandyopadhyay, S., An efficient for superfamily classification of amino acid sequences: feature extraction, fuzzy clustering and prototype selection. Fuzzy Sets and Systems 152 (2005), 5-16.
  • [15] Casasnovas, J. and Rossell, F., Averaging fuzzy biopolymers. Fuzzy Sets and Systems 152 (2005), 139-158.
  • [16] Chang, B.C. and Halgamuge, S.K., Protein motif extraction with neuro-fuzzy optimization. Bioinformatics 18 (2002), 1084-1090.
  • [17] Dembl, D. and Kastner, P., Fuzzy C-means method for clustering microarray data. Bioinformatics 19 (2003), 973-980.
  • [18] Heger, A. and Halm, L.,Sensitive pattern discovery with fuzzy alignments of distantly related proteins. Bioinformatics 19 (2003), 130-137.
  • [19] Nieto, J.J., Torres, A., Georgiou, D.N. and Karakasidis, T.E., Fuzzy polynucleatide spaces and metrics. Bulletin of Mathematical Biology 68 (2006), 301-317.
  • [20] Kaleva, O., Fuzzy differential inclusions. Fuzzy Sets and Systems 24 (1987), 301-317.
  • [21] Kloeden, P., Remarks on Peano-like theorems for fuzzy differential equations. Fuzzy Sets and Systems 44 (1991), 161-164.
  • [22] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987), 319-330.
  • [23] Song, S. and Wu, C., Existence and uniqueness of solution to the Cauchy problem of fuzzy differential equations. Fuzzy Sets and Systems 110 (2000), 55-67.
  • [24] Wu,C., Song, S. and Stanley Lee, E.,Approximate solution existence and uniqueness of the Cauchy problem of fuzzy differential equations. Journal of Mathematical Analysis and Applications 202 (1996), 629-644.
  • [25] Kaleva, O., The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35 (1990), 389-396.
  • [26] He, Q. and Yi, W., On fuzzy differential equations. Fuzzy Sets and Systems 32 (1989), 321- 325.
  • [27] Menda, W., Linear fuzzy differential equation system on R1 . Journal of Fuzzy Syst Math2(1) (1988), 51-56 (in Chinese).
  • [28] Allahviranloo, T., Ahmadi,N. and Ahmadi, E., Numerical solution of fuzzy differential equations by predictor-corrector method. Information sciences 177 (2007), 1633-1647.
  • [29] Friedman,M., Ma, M. and Kandel, A., Numerical solution of fuzzy differential and integral equations. Fuzzy Sets and Systems 106 (1999), 35-45.
  • [30] Ma, M., Friedman, M. and Kandel, A., Numerical solution of fuzzy differential equations. Fuzzy Sets and Systems 105 (1999), 133-138.
  • [31] Khastan, A. and Ivaz, K., Numerical solution of fuzzy differential equations by Nystr¨om method. Chaos, Solitons and Fractals 41 (2009), 859-865.
  • [32] Isaacson, E. and Keller, H.B.,Analysis of Numerical Methods, Wiley, New York, 1966. [33] Stefanini, L.,Sorini, L. and Guerra, M.L., Parametric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets and Systems 157 (2006),2423-2455.
  • [34] Dong-Kai, Z., Wen-Li, F., Ji-qing, Q. and Duoming, X., On the study of linear properties for fuzzy number-valued fuzzy integrals. Fuzzy Information and Engineering 54 (2009),227-232.
  • [35] Colombo, G. and Krivan, V.,Fuzzy differential inclusions and non-probabilistic likelihood. Dynamic Systems and Applications 1 (1992),419-440.
  • [36] Kaleva, O.,Interpolation of fuzzy data. Fuzzy Sets and Systems 35 (1990),389-396.
  • [37] Effati, S. and Pakdaman, M., Artificial neural network approach for solving fuzzy differential equations. Information Sciences 180 (2010),1434-1457.
  • [38] Abu-Argub, O., El-Ajou, A., Momani, S.and Shawagfeh, N.,Analytical solutions of fuzzy initial value problems by HAM. Applied Mathematics and Information Sciences 5 (2013),1903- 1909.

NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD

Year 2015, Volume: 3 Issue: 1, 137 - 153, 15.05.2015

Mine Aylin Bayrak Emine Can

https://doi.org/10.36753/mathenot.421232

Abstract

In this paper Milne’s predictor-corrector method to solve the fuzzy
first first-order initial value problem are investigated. Sufficiently conditions
for stability and convergence of the proposed algorithm are also proved. Their
applicability is illustrated by two examples.

Keywords

Fuzzy differential equations Fuzzy initial value problem Predictorcorrector method Milne’s method

References

  • [1] Guo, M., Xue, X. and Li, R., Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets and Systems 138 (2003), 601-615.
  • [2] El Naschie, M.S., A review of E-infinite theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 19 (2004), 209-236.
  • [3] El Naschie, M.S., The concepts of E-infinite: an elementary introduction to the Cantorianfractal theory of quantum physics. Chaos, Solitons and Fractals 22 (2004), 495-511.
  • [4] El Naschie, M.S., On a fuzzy Khler manifold which is consistent with the two slit experiment. International Journal of Nonlinear Science Numerical Simulation 6 (2005), 95-98.
  • [5] Tanaka,Y., Mizuna Y. and Kado, T., Chaotic dynamics in the Friedman equation. Chaos, Solitons and Fractals 24 (2005), 407-422.
  • [6] El Naschie, M.S., From experimental quantum optics to quantum gravity via a fuzzy Khler manifold. Chaos, Solitons and Fractals 25 (2005), 969-977.
  • [7] Zhang, H., Liao, X. and Yu, J., Fuzzy modelling and synchronization of hyperchaotic systems. Chaos, Solitons and Fractals 26 (2005), 835-843.
  • [8] Feng, G. and Chen, G., Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos, Solitons and Fractals 23 (2005), 459-467.
  • [9] Jiang, W., Guo-Dang, Q. and Bin, D., H∞ variable universe adaptive fuzzy control for chaotic systems. Chaos, Solitons and Fractals 24 (2005), 1075-1086.
  • [10] Abbad, M.F.,Von Keyserlingk, D.G.,Linkens, D.A. and Mahfouf,M., Survey of utilisation of fuzzy technology in medicine and healthcare. Fuzzy Sets and Systems 120 (2001), 331-349.
  • [11] Barro, S. and Marn, R.,Fuzzy logic in medicine,Heidelberg, Physica-verlag,2002.
  • [12] Helgason, C.M. and Jobe, T.H., The fuzzy cube and causal efficiacy: representation of concomitant mechanisms in stroke. Neural Networks 11 (1998), 549-555.
  • [13] Nieto, J.J. and Torres, A., Midpoints for fuzzy sets and their application in medicine. Artificial Intelligence in Medicine 27 (2003), 81-101.
  • [14] Bandyopadhyay, S., An efficient for superfamily classification of amino acid sequences: feature extraction, fuzzy clustering and prototype selection. Fuzzy Sets and Systems 152 (2005), 5-16.
  • [15] Casasnovas, J. and Rossell, F., Averaging fuzzy biopolymers. Fuzzy Sets and Systems 152 (2005), 139-158.
  • [16] Chang, B.C. and Halgamuge, S.K., Protein motif extraction with neuro-fuzzy optimization. Bioinformatics 18 (2002), 1084-1090.
  • [17] Dembl, D. and Kastner, P., Fuzzy C-means method for clustering microarray data. Bioinformatics 19 (2003), 973-980.
  • [18] Heger, A. and Halm, L.,Sensitive pattern discovery with fuzzy alignments of distantly related proteins. Bioinformatics 19 (2003), 130-137.
  • [19] Nieto, J.J., Torres, A., Georgiou, D.N. and Karakasidis, T.E., Fuzzy polynucleatide spaces and metrics. Bulletin of Mathematical Biology 68 (2006), 301-317.
  • [20] Kaleva, O., Fuzzy differential inclusions. Fuzzy Sets and Systems 24 (1987), 301-317.
  • [21] Kloeden, P., Remarks on Peano-like theorems for fuzzy differential equations. Fuzzy Sets and Systems 44 (1991), 161-164.
  • [22] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987), 319-330.
  • [23] Song, S. and Wu, C., Existence and uniqueness of solution to the Cauchy problem of fuzzy differential equations. Fuzzy Sets and Systems 110 (2000), 55-67.
  • [24] Wu,C., Song, S. and Stanley Lee, E.,Approximate solution existence and uniqueness of the Cauchy problem of fuzzy differential equations. Journal of Mathematical Analysis and Applications 202 (1996), 629-644.
  • [25] Kaleva, O., The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35 (1990), 389-396.
  • [26] He, Q. and Yi, W., On fuzzy differential equations. Fuzzy Sets and Systems 32 (1989), 321- 325.
  • [27] Menda, W., Linear fuzzy differential equation system on R1 . Journal of Fuzzy Syst Math2(1) (1988), 51-56 (in Chinese).
  • [28] Allahviranloo, T., Ahmadi,N. and Ahmadi, E., Numerical solution of fuzzy differential equations by predictor-corrector method. Information sciences 177 (2007), 1633-1647.
  • [29] Friedman,M., Ma, M. and Kandel, A., Numerical solution of fuzzy differential and integral equations. Fuzzy Sets and Systems 106 (1999), 35-45.
  • [30] Ma, M., Friedman, M. and Kandel, A., Numerical solution of fuzzy differential equations. Fuzzy Sets and Systems 105 (1999), 133-138.
  • [31] Khastan, A. and Ivaz, K., Numerical solution of fuzzy differential equations by Nystr¨om method. Chaos, Solitons and Fractals 41 (2009), 859-865.
  • [32] Isaacson, E. and Keller, H.B.,Analysis of Numerical Methods, Wiley, New York, 1966. [33] Stefanini, L.,Sorini, L. and Guerra, M.L., Parametric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets and Systems 157 (2006),2423-2455.
  • [34] Dong-Kai, Z., Wen-Li, F., Ji-qing, Q. and Duoming, X., On the study of linear properties for fuzzy number-valued fuzzy integrals. Fuzzy Information and Engineering 54 (2009),227-232.
  • [35] Colombo, G. and Krivan, V.,Fuzzy differential inclusions and non-probabilistic likelihood. Dynamic Systems and Applications 1 (1992),419-440.
  • [36] Kaleva, O.,Interpolation of fuzzy data. Fuzzy Sets and Systems 35 (1990),389-396.
  • [37] Effati, S. and Pakdaman, M., Artificial neural network approach for solving fuzzy differential equations. Information Sciences 180 (2010),1434-1457.
  • [38] Abu-Argub, O., El-Ajou, A., Momani, S.and Shawagfeh, N.,Analytical solutions of fuzzy initial value problems by HAM. Applied Mathematics and Information Sciences 5 (2013),1903- 1909.
There are 37 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mine Aylin Bayrak

Emine Can This is me

Publication Date May 15, 2015
Submission Date January 9, 2015
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Bayrak, M. A., & Can, E. (2015). NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD. Mathematical Sciences and Applications E-Notes, 3(1), 137-153. https://doi.org/10.36753/mathenot.421232
AMA Bayrak MA, Can E. NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD. Math. Sci. Appl. E-Notes. May 2015;3(1):137-153. doi:10.36753/mathenot.421232
Chicago Bayrak, Mine Aylin, and Emine Can. “NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 137-53. https://doi.org/10.36753/mathenot.421232.
EndNote Bayrak MA, Can E (May 1, 2015) NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD. Mathematical Sciences and Applications E-Notes 3 1 137–153.
IEEE M. A. Bayrak and E. Can, “NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 137–153, 2015, doi: 10.36753/mathenot.421232.
ISNAD Bayrak, Mine Aylin - Can, Emine. “NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD”. Mathematical Sciences and Applications E-Notes 3/1 (May 2015), 137-153. https://doi.org/10.36753/mathenot.421232.
JAMA Bayrak MA, Can E. NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD. Math. Sci. Appl. E-Notes. 2015;3:137–153.
MLA Bayrak, Mine Aylin and Emine Can. “NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 137-53, doi:10.36753/mathenot.421232.
Vancouver Bayrak MA, Can E. NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS BY MILNE’S PREDICTOR-CORRECTOR METHOD. Math. Sci. Appl. E-Notes. 2015;3(1):137-53.

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