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A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton’s method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.

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Acknowledgements

The authors thank the anonymous referees and editor for their valuable time, effort and extensive comments which help to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics Education, Faculty of Muallim Rifat Education, Kilis 7 Aralik University, Kilis, Turkey

    Bilge Inan

  2. Department of Mathematics, Faculty of Arts and Science, Inonu University, Malatya, Turkey

    Ahmet Refik Bahadir

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  1. Bilge Inan
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  2. Ahmet Refik Bahadir
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Correspondence to Bilge Inan.

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Inan, B., Bahadir, A.R. A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 299–308 (2020). https://doi.org/10.1007/s40010-019-00594-8

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  • DOI: https://doi.org/10.1007/s40010-019-00594-8

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