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The New General Integral Transform Decomposition method for solving nonlinear Volterra integral equation based on Numerical formula
Subject area: Science,Engineering and Technology · Area of research: Applied Mathematics
Abstract
In this paper, we propose a new method, namely New General Integral Decomposition method (GIDM) for solving nonlinear Volterra integral equations. This method is a combination of the new general integral transform method and decomposition method. The nonlinear terms can be easily handled by the use of A domian polynomials. The technique is described and illustrated with some examples. The resultsreveal that the proposed method is very efficient, simple and can beapplied to other nonlinear problems.
Keywords
New General integral decomposition method, Nonlinear integral equations, Adomian polynomials, Noise terms phenomena.
References
[1] Jafari H. ,A new general integral transform for solving integral equations, Journal of Advanced Research,32(2021),133-138.
[2] Aboodh KS. The new integral transform aboodh transform. Global J Pure ApplMathe 2013;9(1):35–43.
[3] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Acad. Publ., Boston, 1994.
[4] A.M. Wazwaz, A new technique for calculating Adomian polynomials for nonlinear polynomials, Appl. Math. Compt., 111 (2002), 33-51.
[5] S.A. Khuri, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, Journal of Applied Mathematics, 1 (2001),141–155.
[6] S. Abbasbandy, Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation 145 (2003) 887–893.
How to cite this paper
@article{1704001,
author = {Harshwardhan S. Pandharkar, Dr. V. E. Nikumbh},
title = {The New General Integral Transform Decomposition method for solving nonlinear Volterra integral equation based on Numerical formula},
journal = {Iconic Research And Engineering Journals},
year = {2023},
volume = {6},
number = {7},
pages = {105-109},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1704001.pdf},
abstract = {In this paper, we propose a new method, namely New General Integral Decomposition method (GIDM) for solving nonlinear Volterra integral equations. This method is a combination of the new general integral transform method and decomposition method. The nonlinear terms can be easily handled by the use of A domian polynomials. The technique is described and illustrated with some examples. The resultsreveal that the proposed method is very efficient, simple and can beapplied to other nonlinear problems.},
keywords = {New General integral decomposition method, Nonlinear integral equations, Adomian polynomials, Noise terms phenomena.},
month = {January},
}