A numerical solution of the MEW equaiton using sextic B splines

In this article, a numerical solution of the modified equal width wave (MEW) equation, based on subdomain method using sextic B-spline is used to simulate the motion of single solitary wave and interaction of two solitary waves. The three invariants of the motion are calculated to determine the conservation properties of the system. L2 and L∞ error norms are used to measure differences between the analytical and numerical solutions. The obtained results are compared with some published numerical solutions. A linear stability analysis of the scheme is also investigate

Subdomain finite element method with quartic B-splines for the modified equal width wave equation

In this paper, a numerical solution of the modified equal width wave (MEW) equation, has been obtained by a numerical technique based on Subdomain finite element method with quartic Bsplines. Test problems including the motion of a single solitary wave and interaction of two solitary waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable

Petrov galerkin method with cubic B splines for solving the MEW equation

In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin method in which the element shape functions are cubic B-splines and the weight functions quadratic B-splines . The motion of a single solitarywave and interaction of two solitarywaves are studied. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and L2 , L¥ error norms. The obtained results show that the present method is a remarkably successful numerical technique for solving the modified equal width wave(MEW) equation. A linear stability analysis of the scheme shows that it is unconditionally stable

Septic B spline collocation method for the numerical solution of the modified equal width wave equation

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

Numerical solution of the modified equal width wave equation

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 L2 and L∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated

An Accurate Numerical Solution for the Modified Equal Width Wave Equation Using the Fourier Pseudo-Spectral Method

Abstract In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L2 and L∞ error norms are computed to study the accuracy and the simplicity of the presented method