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2020•Journal of Physics Conference SeriesOpen access

Semi-Analytical Method with Laplace Transform for Certain Types of Nonlinear Problems

Areej Salah Mohammed, Sinan Hatif Abd Almjeed

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Abstract

Abstract In this paper, the approximate solution is found for the Fornberg-Whitham equation (F-W) by using two analytical methods which are the Laplace decomposition method (LDM) and modified Laplace decomposition method (MLDM) with comparison between these methods for which gave the best approximate solution near to the exact solution, The analytical results of these methods have been received in terms of convergent series with easily calculable components. The results show that the modified method was found to be efficient, accurate and fast compared to the second method used in this research.

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Abstract In this paper, the approximate solution is found for the Fornberg-Whitham equation (F-W) by using two analytical methods which are the Laplace decomposition method (LDM) and modified Laplace decomposition method (MLDM) with comparison between these methods for which gave the best approximate solution near to the exact solution, The analytical results of these methods have been received in terms of convergent series with easily calculable components. The results show that the modified method was found to be efficient, accurate and fast compared to the second method used in this research.

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Available abstract

Abstract In this paper, the approximate solution is found for the Fornberg-Whitham equation (F-W) by using two analytical methods which are the Laplace decomposition method (LDM) and modified Laplace decomposition method (MLDM) with comparison between these methods for which gave the best approximate solution near to the exact solution, The analytical results of these methods have been received in terms of convergent series with easily calculable components. The results show that the modified method was found to be efficient, accurate and fast compared to the second method used in this research.

Key concepts: Laplace transform, Convergent series, Decomposition method (queueing theory), Laplace transform applied to differential equations, Series (stratigraphy), Decomposition, Mathematics, Applied mathematics

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