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Exponential B-Splines for Numerical Solutions to Some Boussinesq Systems for Water Waves

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Abstract

In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one-dimensional Boussinesq systems numerically. Two initial boundary value problems for Regularized and Classical Boussinesq systems modeling motion of traveling waves are considered. The accuracy of the method is validated by measuring the error between the numerical and analytical solutions. The numerical solutions obtained by various values of free parameter \({\zeta}\) are compared with some solutions in literature. Numerical behavior of solitary waves under small perturbations is also studied.

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Authors and Affiliations

  1. Department of Mathematics-Computer, Eskişehir Osmangazi University, 26480, Eskişehir, Turkey

    Ozlem Ersoy

  2. Department of Mathematics, Çankırı Karatekin University, 18200, Çankırı, Turkey

    Alper Korkmaz

  3. Department of Computer Engineering, Eskişehir Osmangazi University, 26480, Eskişehir, Turkey

    Idiris Dağ

Authors
  1. Ozlem Ersoy
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  2. Alper Korkmaz
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  3. Idiris Dağ
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Correspondence to Ozlem Ersoy.

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Ersoy, O., Korkmaz, A. & Dağ, I. Exponential B-Splines for Numerical Solutions to Some Boussinesq Systems for Water Waves. Mediterr. J. Math. 13, 4975–4994 (2016). https://doi.org/10.1007/s00009-016-0787-4

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  • DOI: https://doi.org/10.1007/s00009-016-0787-4

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