A mixed method approach to the solitary wave, undular bore and boundary-forced solutions of the Regularized Long Wave equation

BAŞHAN A., YAĞMURLU N. M.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.41, sa.4, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s40314-022-01882-7
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Anahtar Kelimeler: Finite difference method, Differential quadrature method, RLW equation, Convergence, FINITE-ELEMENT-METHOD, CUBIC B-SPLINES, NUMERICAL-SOLUTION, RLW EQUATION, DIFFERENTIAL QUADRATURE, GALERKIN METHOD, BURGERS-EQUATION, NONLINEAR VARIANTS, ALGORITHM, EXPLICIT
  • İnönü Üniversitesi Adresli: Evet

Özet

The aim of the present work is to obtain numerical solutions of the solitary wave, undular bore and boundary-forced problems for Regularized Long Wave (RLW) equation. For this purpose, low-order modified cubic B-spline is chosen as base functions. Crank-Nicolson formulae combined with efficient space discretization method have been applied. With the aid of Rubin and Graves type linearization technique, nonlinear terms are linearized and a solvable linear equation system has been obtained. Three significant test problems in the literature are solved successfully. The present algorithm has obtained high accurate numerical solutions of the RLW equation. Numerical results are compared with those of some earlier ones and given. The rates of the convergence are also investigated.