...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 45 | Number 1 | Year 2017 | Article Id. IJMTT-V45P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V45P506

Numerical Solution of Non-linear Fuzzy Differential Equations using Single Term Walsh Series Technique


A. EmimalKanaga Pushpam, P. Anandhan
Abstract

This paper presents Single Term Walsh Series Technique (STWS) to obtain the numerical solution of non-linear fuzzy differential equations (FDEs). The applicability of this technique is illustrated through two examples. The numerical results are compared with their exact solutions.

Keywords
Fuzzy differential equations, non-linear, IVP, STWS.
References

[1] S. Abbasbandy, T. Allahviranloo, Numerical solution of fuzzy differential equation by Taylor method, Journal of Computational Methods in Applied mathematics, 2 (2002) 113-124.
[2] S. Abbasbandy, T. Allahviranloo, Numerical solution of fuzzy differential equation, Mathematical and Computational Applications, 7 (2002) 41-52.
[3] S. Abbasbandy, T. Allahviranloo, Numerical solution of fuzzy differential equation by Runge-Kutta method, Nonlinear Studies, 11 (2004) 117-129.
[4] T. Allahviranloo, N. Ahmady, E. Ahmady, Numerical solution of fuzzy differential equations by predictor- Corrector method, Information Sciences, 177 (2007) 1633- 1647.
[5] T. Allahviranloo, S. Abbasbandy N. Ahmady, E. Ahmady, Improved predictor-Corrector method for solving fuzzy initial value problems, Information Sciences, 179 (2009) 945-955.
[6] K. Balachandran, K. Murugesan, Analysis of different systems via Single term Walsh series method, International Journal of Computer Mathematics, 33 (1990) 171–179.
[7] K. Balachandran, K. Murugesan, Analysis of non-linear singular systems via STWS method, International Journal of Computer Mathematics, 36, (1990) 9–12.
[8] S. L. Chang and L. A. Zadeh, On Fuzzy Mapping and Control, IEEE Trans. Systems, Man, and Cybernet, 2 (1972) 30-34.
[9] A. EmimalKanagaPushpam , D. Paul Dhayabaran, E.C. Henry Amirtharaj, Numerical solution of higher order systems of IVPs using generalized STWS technique, Applied Mathematics and Computation, 180 (2006)200–205.
[10] A. EmimalKanagaPushpam, D. Paul Dhayabaran, An Application of STWS Technique in Solving Stiff Non-linear System: High Irradiance Responses (HIRES) of Photo morphogenesis, Recent Research in Science and Technology, 3(6) (2011) 47-53.
[11] A. EmimalKanagaPushpam, P. Anandhan, Numerical Solution of Higher Order Linear Fuzzy Differential Equations using Generalized STWS Technique, International J. Innovative Research in Science, Eng. and Technology (IJIRSET), 5(3) (2016) 3862 - 3869.
[12] A. EmimalKanagaPushpam, P. Anandhan, Solving Higher Order Linear System of Time Varying Fuzzy Differential Equations using Generalized STWS Technique, International Journal of Science and Research, 5(4) (2016) 57 – 61.
[13] T. Jayakumar, D. Maheshkumar, K. Kanagarajan, Numerical solution of fuzzy differential equations by Runge-Kutta method order five, International Journal of Applied Mathematical Science, 6 (2012) 2989-3002.
[14] T. Jayakumar, C.Raja, T.Muthukumar, Numerical solution of fuzzy differential equations by Adams fifth order predictorcorrector method, International Journal of Mathematics Trends and Technology (2014) 1-18.
[15] O. Kaleva, Fuzzy Differential Equations, Fuzzy Sets Systems, 24 (1987) 301-317.
[16] O. Kaleva, The Cauchy problem for Fuzzy Differential Equations, Fuzzy Sets Systems, 35 (1990) 389-396.
[17] K. Kanagarajan, S. Muthukumar, S. Indrakumar Numerical solution of fuzzy differential equations by Extended Runge- Kutta Method and the Dependency Problem, International Journal of mathematics Trends and Technology 6(2014) 113-122.
[18] K. Kanagarajan, M. Sambath, Numerical solution of fuzzy differential equations by third order Runge-Kutta method, International Journal of Applied Mathematics and Computation, 2 (2010) 1-10.
[19] K. Murugesan, D. P. Dhayabaran, D. J. Evans, Analysis of second order multivariable linear system using Single-term Walsh series technique and Runge Kutta method, International Journal of Computer Mathematics, 72 (1999) 367–374.
[20] D. Paul Dhayabaran, A. EmimalKanagaPushpam, E.C. Henry Amirtharaj, Generalized STWS technique for higher order time-varying singular systems, International Journal of Computer Mathematics, 84 (2007) 395–402.
[21] G. P. Rao, K. R. Palanisamy, T. Srinivasan, Extension of computation beyond the limit of normal interval in Walsh series analysis of dynamical systems, IEEE. Trans. Automat. Contr., 25(1980) 317–319.
[22] S. Seikkala, On the Fuzzy Initial Value Problem, Fuzzy Sets Systems, 24 (1987)319-330.
[23] B. Sepehrian and M. Razzaghi, Solution of time-varying singular nonlinear systems by Single-term Walsh series, Mathematical Problems in Engineering 2003, 3 (2003), 129–136.
[24] S. Sekar, S. Senthilkumar, Single Term Haar Wavelet series forfuzzy differential equations, International Journal of Mathematics Trends and Technology 4 (9)( 2013), 181-188.

Citation :

A. EmimalKanaga Pushpam, P. Anandhan, "Numerical Solution of Non-linear Fuzzy Differential Equations using Single Term Walsh Series Technique," International Journal of Mathematics Trends and Technology (IJMTT), vol. 45, no. 1, pp. 35-39, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V45P506

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved