The New Combination of Semi-Analytical Iterative Method and Elzaki Transform for Solving Some Korteweg-de Vries Equations
Keywords:
Elzaki transformation, semi-analytical iterative method, Korteweg-de Vries equations, approximate analytical solutions
Abstract
The purpose of this research applied a method that includes the combination of an iterative method (Temimi and Ansari method (TAM)) and a new transform called the Elzaki transform (ET )for some Korteweg-de Vries (Kdv) equations. The TAM was present as a basic tool for solving Kdv equations with Elzaki transformation in the associated nonlinear equations because the Elzaki transformation cannot deal with nonlinear terms. It has been proven that the use of this method can be more reliable, accurate and fast if it has been using analytical methods alone.
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References
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[2] AL-Jawary. M.A.; Mohammed.A.S. A Semi-Analytical Iterative Method for Solving Linear and Nonlinear Partial Differential Equations. International Journal of Science and Research. 2017, 6, 5,978-982.
[3] Tawfiq. L. N.; Hasan. M. A. Evaluate the Rate of Pollution in Soil using Simulink Environment. Ibn Al Haitham Journal for Pure and Applied Science. 2019, 32, 1, 132-138.
[4] Adnan.F.A.; Abdul Hadi A. M. Peristaltic Flow of the Bingham Plastic Fluid in a Curved Channel. Ibn Al Haitham Journal for Pure and Applied Science. 2019, 32, 3, 140-152.
[5] Kaya.D.; Aassila. M. An application for a generalized KdV equation by the decomposition method. Physics Letters A. 2002, 299, 2–3, 201-206.
[6] Mirgolbabaei. H.; Ganji. D.D. Application of Homotopy Perturbation Method to Solve Combined Korteweg de Vries-Modified Korteweg de Vries Equation. Journal of Applied Sciences. 2009, 9, 19, 3587-3592.
[7] Yassein. S. M.; Aswhad. A. A. Efficient Iterative Method for Solving Korteweg-de Vries Equations. Iraqi Journal of Science. 2019, 60, 7, 1575-1583.
[8] Hendi. F.A. Laplace Adomian Decomposition Method for Solving the Nonlinear Volterra Integral Equation with Weakly Kernels. Studies in Nonlinear Sciences. 2011, 2, 4, 129-134.
[9] Ahmed.Sh.Sh.; Salih. Sh. A. H.; Ahmed. M. R. Laplace Adomian and Laplace Modified Adomian Decomposition Methods for Solving Nonlinear Integro-Fractional Differential Equations of the Volterra-Hammerstein Type. Iraqi Journal of Science. 2019, 60, 10, 2207-2222.
[10] Eljaily. M. H.; Elzaki. T. M. Homotopy Perturbation Transform Method for Solving (KDV) Equation, Pure and Applied Mathematics Journal. 2015, 4, 6, 264-268.
[11] Suleman. M.; Wu. Q.; Abbas. Gh. Approximate analytic solution of (2 + 1) dimensional coupled differential Burger’s equation using Elzaki Homotopy Perturbation Method. Alexandria Engineering Journal. 2016, 55, 2, 1817–1826.
[12] Nuruddeen. R. I.; Nass. A. M. Aboodh Decomposition Method and its Application in Solving Linear and Nonlinear Heat Equations. European Journal of Advances in Engineering and Technology. 2016, 3, 7, 34-37.
[13] Elzaki. T. M.; Chamekh. M. Solving Nonlinear Fractional Differential Equations using a New Decomposition Method. Universal Journal of Applied Mathematics & Computation. 2018, 6, 27-35
[14] Elijah. I. O. Approximate Analytical Solution of Nonlinear Differential Equations using Elzaki Transform. Case study: Korteweg-de Vries (KdV) Equations. Master’s Thesis, Lappeenranta University of Technology, 2018.
[15] Temimi. H.; Ansari. A. R. A Semi Analytical Iterative Technique for Solving Nonlinear Problems. Computers and Mathematics with Applications. 2011, 61, 2, 203- 210.
[16] Elzaki. T. M. The New Integral Transform ''ELzaki Transform''. Global Journal of Pure and Applied Mathematics. 2011, 7, 1, 57–64.
Published
2020-02-25
How to Cite
Salah, A. (2020). The New Combination of Semi-Analytical Iterative Method and Elzaki Transform for Solving Some Korteweg-de Vries Equations. Al-Qadisiyah Journal of Pure Science, 25(1), Math. 23 -. https://doi.org/10.29350/jops.2020.25.1.1063
Issue
Section
Mathematics
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