Solving three-dimensional Volterra integral equation by the reduced differential transform method
DOI:
https://doi.org/10.14419/ijamr.v5i2.5988Keywords:
Volterra integral equation, Differential transform, Reduce differential transform.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.
References
[1]
R. Abazari, A. Kiliçman â€Numerical study of two-dimensional Volterra integral equation by RDTM and comparison with DTMâ€, Abstr Appl Anal Volume 2013, (2013), doi.org/101155/2013/929478.
[2]
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.
[3]
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
[4]
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.
[5]
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. }
[6]
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.
[7]
R.P. Kanwal, Linear Integral Equations, Springer Science and Business Media, 2013.
[8]
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.
[9]
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
[10]
F. Mohammadi, "A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations", Int J Appl Math Research, 4 (2), (2015) 217-227.
[11]
R. Rahman, Integral Equations and Their Applications, Wit Pr/Computational Mechanics, 2007.
[12]
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), http://dx.doi.org/10.1016/j.jksues.2014.04.010.
[13]
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
[14]
A.M. Wazwaz, Linear and nonlinear integral equations: methods and applications, Springer Science and Business Media, 2011.
Downloads
How to Cite
Received date: March 9, 2016
Accepted date: April 11, 2016
Published date: April 19, 2016