Solving three-dimensional Volterra integral equation by the reduced differential transform method
Keywords:Volterra integral equation, Differential transform, Reduce differential transform.
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.
R. Abazari, A. KiliÃ§man 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.
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), http://dx.doi.org/10.1016/j.jksues.2014.04.010.
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.
View Full Article:
Authors who publish with this journal agree to the following terms:
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under aÂ Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (SeeÂ The Effect of Open Access).