Application of Homotopy Perturbation Method for Fuzzy Integral Equations

Volume 1, Issue 4, pp 377--385 http://dx.doi.org/10.22436/jmcs.001.04.15

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2106 Downloads
• 3302 Views

Authors

Mashallah Matinfar - Department of Mathematics, University of Mazandaran, Iran Mohammad Saeidy - Department of Mathematics, University of Mazandaran, Iran

Abstract

In this paper, an application of homotopy perturbation method (HPM) is applied to solve linear fuzzy Fredholm integral equation. Comparison are made between the exact solution and solution of homotopy perturbation method. The results reveal that the homotopy analysis method is very effective and simple.

Share and Cite

Keywords

• Fuzzy number
• Fredholm integral equation
• Homotopy perturbation method.

MSC

•  93C73
•  03E72
•  45B05

References

• [1] E. Babolian, H. Sadeghi Goghary, S. Abbasbandy, Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method, Appl. Math. Comput., 161 (2005), 733--744
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] C. Wu, M. Ma, On the integrals, series and integral equations of fuzzy set valued functions, J. Harbin. Inst. Technol., 21 (1990), 11--19
  • View Article
  • Google Scholar


• [3] J. H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178 (1999), 257--262
  • View Article
  • MathSciNet
  • Google Scholar


• [4] J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg., 167 (1998), 57--68
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] J. H. He, Comparison of homotopy perturbtaion method and homotopy analysis Method, Appl. Math. Comput., 156 (2004), 527--539
  • View Article
  • Google Scholar


• [6] J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-Linear Mech., 35 (2000), 37--43
  • View Article
  • Google Scholar
  • MATH


• [7] J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput., 135 (2003), 73--79
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] J. H. He, Some asymptotic methods for strongly nonlinear equations, Int .J. Mod .Phys. B, 20 (2006), 1141--1199
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] J. J. Buckley, Fuzzy eigenvalues and inputoutput analysis, Fuzzy Sets and Systems, 34 (1990), 187--195
  • View Article
  • Google Scholar


• [10] M. L. Puri, D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl., 114 (1986), 409--422
  • View Article
  • MathSciNet
  • Google Scholar


• [11] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039--1046
  • View Article
  • MathSciNet
  • Google Scholar


• [12] R. Zhao, R. Govind, Solutions of algebraic equations involving generalized fuzzy number, Inform. Sci., 56 (1991), 199--243
  • View Article
  • MathSciNet
  • Google Scholar


• [13] R. Goetschel, W. Voxman, Eigen fuzzy number sets, Fuzzy Sets and Systems, 16 (1985), 75--85
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] S. S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Trans. Syst. Man Cybern., 2 (1972), 30--34
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH