Numerical solution of the regularized long wave equation using nonpolynomial splines

In this paper, we employ nonpolynomial spline (NPS) basis functions to obtain approximate solutions of the regularized long wave (RLW) equation. By considering suitable relevant parameters, it is shown that the local truncation error behaves O ( k 2 + h 2 ) with respect to the time and space discret...

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Bibliographic Details
Published in:Nonlinear dynamics 2012-07, Vol.69 (1-2), p.459-471
Main Authors: Chegini, N. G., Salaripanah, A., Mokhtari, R., Isvand, D.
Format: Article
Language:English
Subjects:
Approximation
Automotive Engineering
Basis functions
Classical Mechanics
Control
Discretization
Dynamical Systems
Energy conservation
Engineering
Initial conditions
Mathematical analysis
Mathematical models
Mechanical Engineering
Numerical stability
Original Paper
Solitary waves
Splines
Stability analysis
Truncation errors
Vibration
Wave equations
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Summary:In this paper, we employ nonpolynomial spline (NPS) basis functions to obtain approximate solutions of the regularized long wave (RLW) equation. By considering suitable relevant parameters, it is shown that the local truncation error behaves O ( k 2 + h 2 ) with respect to the time and space discretization. Numerical stability of the method is investigated by using a linearized stability analysis. To illustrate the applicability and efficiency of the aforementioned basis, we compare obtained numerical results with other existing recent methods. Motion of single solitary wave and double and triple solitary waves, wave undulation, generation of solitary waves using the Maxwellian initial condition and conservation properties of mass, energy, and momentum of numerical solutions of the equation are dealt with.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-011-0277-y