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

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ERSOY HEPSON Ö., KORKMAZ A., DAĞ İ.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.13, no.6, pp.4975-4994, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.1007/s00009-016-0787-4
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4975-4994
  • Keywords: Boussinesq systems, solitary waves, exponential cubic B-spline, collocation, wave generation, COLLOCATION METHOD, EQUATIONS
  • Eskisehir Osmangazi University Affiliated: Yes

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 are compared with some solutions in literature. Numerical behavior of solitary waves under small perturbations is also studied.