Novel algorithm based on modification of Galerkin finite element method to general Rosenau-RLW equation in (2 + 1)-dimensions

• Published in: Applied numerical mathematics Vol. 148; pp. 109 - 130
• Main Authors: Tamang, N., Wongsaijai, B., Mouktonglang, T., Poochinapan, K.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2020
• Subjects: Finite element method; Rosenau-RLW equation; Shallow water wave equation; Finite element method; Shallow water wave equation; Rosenau-RLW equation
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2019.07.021

In this research, the presented method combines advantages of the finite element and three-level finite difference techniques to obtain the solution of the two-dimensional general Rosenau-RLW equation. An important point is that nevertheless the two-dimensional general Rosenau-RLW is a non-linear equation, but with the proposed scheme we are able to linearize this system and efficiently solve it due to the implicit nature of the system of equations. In addition, the existence and uniqueness of the approximate solution are approved. The convergence and stability of the approximate solution are also examined. The general formulation of the procedure is given and numerical results are carried out to confirm the accuracy of our theoretical results and the efficiency of the scheme.