Abstract
Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.
Highlights
Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques
This study is concerned with the numerical solution, using septic B-spline functions in collocation method, of the modified equal width wave (MEW) equation, which was introduced by Morrison et al [1] as a model equation to describe the nonlinear dispersive waves
A numerical solution of the MEW equation based on the septic B-spline finite element has been presented with three different linearization techniques
Summary
This study is concerned with the numerical solution, using septic B-spline functions in collocation method, of the modified equal width wave (MEW) equation, which was introduced by Morrison et al [1] as a model equation to describe the nonlinear dispersive waves. Zaki considered the solitary wave interactions for the MEW equation by Petrov-Galerkin method using quintic B-spline finite elements [5] and obtained the numerical solution of the EW equation by using least-squares method [6]. Esen applied a lumped Galerkin method based on quadratic B-spline finite element has been used for solving the EW and MEW equation [8,9]. R. Raslan [14] studied the generalized EW equation by using collocation method based on quadratic B-splines to obtain the numerical solutions of a single solitary waves, and the birth of solitons.
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