| Volume 7, Number 2, 2017, Pages 617-631 DOI：10.11948/2017038 |
| Quadratic trigonometric b-spline galerkin methods for the regularized long wave equation |
| Dursun Irk,Pinar Keskin |
| Keywords:Finite element method, spline approximation, solitary waves equation. |
| Abstract: |
| In this study, a numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on two and three steps Adams Moulton method for the time integration and quadratic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves. For the first test problem, the rate of convergence and the running time of the proposed algorithms are computed and the error norm $L_{\infty }$ is used to measure the differences between exact and numerical solutions. The three conservation quantities of the motion are calculated to determine the conservation properties of the proposed algorithms for both of the test problems. |
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