Highly accurate numerical scheme based on polynomial scaling functions for equal width equation

Oruc O., ESEN A., BULUT F.

WAVE MOTION, cilt.105, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 105
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.wavemoti.2021.102760
  • Dergi Adı: WAVE MOTION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Polynomial scaling, EW equation, Solitary wave, Interaction, B-SPLINE, WAVES
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper we established a numerical method for Equal Width (EW) Equation using Polynomial Scaling Functions. The EW equation is a simpler alternative to well known Korteweg de Vries (KdV) and regularized long wave (RLW) equations which have many applications in nonlinear wave phenomena. According to Polynomial scaling method, algebraic polynomials are used to get the orthogonality between the wavelets and corresponding scaling functions with respect to the Chebyshev weight. First we introduce polynomial scaling functions, how are the functions are approximated according to these and Operational matrix of derivatives are given. For time discretization of the function we use finite difference method with Rubin Graves linearization and polynomial scaling functions are used for the space discretization. The method is applied to four different problem and the obtained results are compared with the results in the literature and with the exact results to give the efficiency of the method. (C) 2021 Elsevier B.V. All rights reserved.