Abstract
Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws and error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.
Highlights
The modified equal width wave equation MEW based upon the equal width wave EW equation 1, 2 which was suggested by Morrison et al 3 is used as a model partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes
Esen applied a lumped Galerkin method based on quadratic B-spline finite elements which have been used for solving the EW and MEW equation 8, 9
The cubic B-spline lumped Galerkin method has been successfully applied to obtain the numerical solution of the modified equal width wave equation
Summary
The modified equal width wave equation MEW based upon the equal width wave EW equation 1, 2 which was suggested by Morrison et al 3 is used as a model partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. Esen applied a lumped Galerkin method based on quadratic B-spline finite elements which have been used for solving the EW and MEW equation 8, 9. Zaki considered the solitary wave interactions for the MEW equation by collocation method using quintic B-spline finite elements and obtained the numerical solution of the EW equation by using least-squares method. A solution based on a collocation method incorporated cubic B-splines is investigated by and Saka and Dag. Variational iteration method is introduced to solve the MEW equation by Lu. Evans and Raslan 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. In the present work we solve the MEW equation numerically by a lumped Galerkin method using cubic B-spline finite elements. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable
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