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Chin. Phys. B, 2015, Vol. 24(5): 050206    DOI: 10.1088/1674-1056/24/5/050206
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Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

Reza Mohammadi
Department of Mathematics, University of Neyshabur, Neyshabur 91136-899, Iran
Abstract  The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of O(k2+h2). Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.
Keywords:  solitary waves      GRLW equation      exponential B-spline      collocation  
Received:  02 November 2014      Revised:  16 December 2014      Published:  05 May 2015
PACS:  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  03.65.Ge (Solutions of wave equations: bound states)  
Corresponding Authors:  Reza Mohammadi     E-mail:  rez.mohammadi@gmail.com, mohammadi@neyshabur.ac.ir
About author:  02.60.Lj; 03.65.Ge

Cite this article: 

Reza Mohammadi Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation 2015 Chin. Phys. B 24 050206

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