Abstract
We introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly.
Highlights
A nonlinear wave phenomenon is the important area of scientific research
We prove the existence and uniqueness of the numerical solution
There are mathematical models which describe the dynamic of wave behaviors such as the KdV equation, the Rosenau equation, and many others
Summary
A nonlinear wave phenomenon is the important area of scientific research. There are mathematical models which describe the dynamic of wave behaviors such as the KdV equation, the Rosenau equation, and many others. Several second-order accuracy finite difference methods in space were used for finding numerical solutions on both linear and nonlinear terms [14,15,16,17,18,19,20]. Hu et al [18] have proposed a three-level average implicit finite difference scheme for the Rosenau-Burgers equation. We propose a modified three-level average linear-implicit finite difference method for the RosenauBurgers equation. By comparing with the existence secondorder accuracy finite difference scheme on a test problem, our new technique gives a better maximal error of the numerical solutions.
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