Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

doi:10.1088/1674-1056/24/5/050206

摘要/Abstract

摘要： 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.

关键词: solitary waves, GRLW equation, exponential B-spline, collocation

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.

Key words: solitary waves, GRLW equation, exponential B-spline, collocation

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

03.65.Ge (Solutions of wave equations: bound states)

Reza Mohammadi. Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation[J]. 中国物理B, 2015, 24(5): 50206-050206.

Reza Mohammadi. Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation[J]. Chin. Phys. B, 2015, 24(5): 50206-050206.

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