80 research outputs found
Numerical approximation to a solution of the modified regularized long wave equation using quintic B splines
In this work, a numerical solution of the modified regularized long wave (MRLW)
equation is obtained by the method based on collocation of quintic B-splines over
the finite elements. A linear stability analysis shows that the numerical scheme based
on Von Neumann approximation theory is unconditionally stable. Test problems
including the solitary wave motion, the interaction of two and three solitary waves
and the Maxwellian initial condition are solved to validate the proposed method by
calculating error norms L2 and L∞ that are found to be marginally accurate and
efficient. The three invariants of the motion have been calculated to determine the
conservation properties of the scheme. The obtained results are compared with other
earlier result
Petrov Galerkin finite element method for solving the MRLW equation
In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave
motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L2, L∞ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigate
Analysis and application of the discontinuous Galerkin method to the RLW equation
In this work, our main purpose is to develop of a sufficiently robust, accurate and efficient numerical scheme for the solution of the regularized long wave (RLW) equation, an important partial differential equation with quadratic nonlinearity, describing a large number of physical phenomena. The crucial idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. Furthermore, a suitable linearization preserves a linear algebraic problem at each time level. We present error analysis of the proposed scheme for the case of nonsymmetric discretization of the dispersive term. The appended numerical experiments confirm theoretical results and investigate the conservative properties of the RLW equation related to mass, momentum and energy. Both procedures illustrate the potency of the scheme consequently.ESF [CZ.1.07/2.3.00/09.0155]; SGS Project 'Modern numerical methods'; TU Libere
An efficient approach to numerical study of the MRLW equation with b spline collocation method
A septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the
proposed method by calculating the error norms \u1d43f��2 and \u1d43f��∞ and the invariants \u1d43c��1, \u1d43c��2, and \u1d43c��3. Also, we have studied the Maxwellian initial condition pulse.The numerical results obtained by the method show that the present method is accurate and efficient. Results
are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated
- …