A sixth-order compact finite difference method for the one-dimensional sine-Gordon equation

Sari M., Gurarslan G.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, cilt.27, sa.7, ss.1126-1138, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 7
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1002/cnm.1349
  • Dergi Adı: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1126-1138
  • Anahtar Kelimeler: sine-Gordon equation, compact finite difference schemes, nonlinear PDE, Runge-Kutta, NUMERICAL-SOLUTION, SCHEME, SOLITONS
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

This paper explores the utility of a sixth-order compact finite difference (CFD6) scheme for the solution of the sine-Gordon equation. The CFD6 scheme in space and a third-order strong stability preserving Runge-Kutta scheme in time have been combined for solving the equation. This scheme needs less storage space, as opposed to the conventional numerical methods, and causes to less accumulation of numerical errors. The scheme is implemented to solve three test problems having exact solutions. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy with minimal computational effort. The present results are also seen to be more accurate than some available results given in the literature. The scheme is seen to be a very reliable alternative technique to existing ones. Copyright (C) 2009 John Wiley & Sons, Ltd.