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Comparison of Exact and Numerical Solutions for the Sharma–Tasso–Olver Equation

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Numerical Solutions of Realistic Nonlinear Phenomena

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 31))

Abstract

In this work, we have considered a Sharma–Tasso–Olver (STO) equation in order to obtain some exact and numerical solutions by using the auto-Bäcklund transformation method (aBTM) and the finite forward difference method. We successfully obtain some kink-type solutions with exponential prototype structure to this equation and also we obtain some numerical solution by using the finite difference method (FDM). We illustrate the comparison between exact and numerical approximations and support the comparison with a graphic plot of these illustrations as well. Moreover, the Fourier–von Neumann stability analysis is used in checking the stability of the numerical scheme. The L 2 and L ∞ error norms of the solutions to this equation are also illustrated here.

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Acknowledgements

The authors of the article would like to thank Istanbul Commerce University and Firat University for supporting this work.

Author information

Authors and Affiliations

  1. Department of Mathematics, Istanbul Commerce University, Istanbul, Turkey

    Doğan Kaya

  2. Department of Actuary, Firat University, Elazig, Turkey

    Asıf Yokuş

  3. Department of Computer Center, Firat University, Elazig, Turkey

    Uğur Demiroğlu

Authors
  1. Doğan Kaya
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  2. Asıf Yokuş
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  3. Uğur Demiroğlu
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Corresponding author

Correspondence to Asıf Yokuş .

Editor information

Editors and Affiliations

  1. Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  2. Department of Mathematics, Balıkesir University, Balıkesir, Turkey

    Necati Özdemir

  3. Department of Mathematics & Computer Science, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

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Kaya, D., Yokuş, A., Demiroğlu, U. (2020). Comparison of Exact and Numerical Solutions for the Sharma–Tasso–Olver Equation. In: Machado, J., Özdemir, N., Baleanu, D. (eds) Numerical Solutions of Realistic Nonlinear Phenomena. Nonlinear Systems and Complexity, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-37141-8_3

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