Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Bashan A., YAĞMURLU N. M., UÇAR Y., ESEN A.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.37, sa.1, ss.690-706, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/num.22547
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.690-706
  • Anahtar Kelimeler: B-splines, differential quadrature method, finite difference method, modified equal width equation, solitary wave, CUBIC B-SPLINES, SOLITON-SOLUTIONS, GALERKIN METHOD
  • İnönü Üniversitesi Adresli: Evet

Özet

The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B-spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.