Solving three-dimensional Volterra integral equation by the reduced differential transform method

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    In this article, the results of two-dimensional reduced differential transform method is extended to three-dimensional case for solving three dimensional Volterra integral equation. Using the described method, the exact solution can be obtained after a few number of iterations. Moreover, examples on both linear and nonlinear Volterra integral equation are carried out to illustrate the efficiency and the accuracy of the presented method.

  • Keywords

    Volterra integral equation, Differential transform , Reduce differential transform.

  • References


      R. Abazari, A. Kiliçman ”Numerical study of two-dimensional Volterra integral equation by RDTM and comparison with DTM”, Abstr Appl Anal Volume 2013, (2013),


      G.A. Afroozi, J. Vahidi, M. Saeidy, "Solving a class of two-dimensional linear and nonlinear Volterra integral equation by means of the homotopy analysis method", Int J Nonlinear Sci, Vol.9 No.2, (2010) 213-219.


      E. Babolian, K. Maleknejad, M. Roodaki, H. Almasieh, "Two-dimensional triangular functions and their applications tononlinear 2D Volterra-Fredholm integral equations", Comput Math Appl, 60(6), (2010) 1711-1722


      M. Bakhshi, Mohhammad Asghari-Larimi, M. Asghari-Larimi, "Three-dimensional differential transform method for solving nonlinear three-dimensional Volterra integral equations", The Journal of Mathematics and Computer Science, Vol. 4 No.2, (2012), 246 - 256.


      N. Dogan, V. Erturk, S. Momani, O. Akin, A. Yildirim, "Differential transform method for solving singularly perturbed Volterra integral equations", Journal of King Saud University- science, 23(2), (2011), 223- 228. }


      B. Jang, "Comments on solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method", J Comput Appl Math, 233(2), (2009)224--230.


      R.P. Kanwal, Linear Integral Equations, Springer Science and Business Media, 2013.


      F. Mirzaee, E. Hadadiyan, S. Bimesl, "Numerical solution for three-dimensional nonlinear mixed Volterra-Fredholm integral equations via three-dimensional block-pulse functions", Appl Math Comput, 237, (2014) 168-175.


      M. M. Moghadam, H.Saeedi, "Application of differential transform for solving the Volterra integro-partial equations", Iran J Sci Technol (Sciences), 34(1), (2010) 59-70


      F. Mohammadi, "A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations", Int J Appl Math Research, 4 (2), (2015) 217-227.


      R. Rahman, Integral Equations and Their Applications, Wit Pr/Computational Mechanics, 2007.


      V.K. Srivastava, M.K. Awasthi, R.K. Chaurasia,reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations, Journal of King Saud University - Engineering Sciences, (2014),


      A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, "Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method", J Comput Appl Math, 228(1), (2009) 70-76


      A.M. Wazwaz, Linear and nonlinear integral equations: methods and applications, Springer Science and Business Media, 2011.




Article ID: 5988
DOI: 10.14419/ijamr.v5i2.5988

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.