A compact finite difference method for solving the general Rosenau-RLW equation

• Main Authors: Wongsaijai,B., Poochinapan,K., Disyadej,T.
• Format: Article
• Published: International Association of Engineers 2015
• Subjects: Applied Mathematics
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84919490710&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38838
• Institution: Chiang Mai University

In this paper, a compact finite difference method to solve the Rosenau-RLW equation is proposed. A numerical tool is applied to the model by using a three-level average implicit finite difference technique. The fundamental conservative property of the equation is preserved by the presented numerical scheme, and the existence and uniqueness of the numerical solution are proved. Moreover, the convergence and stability of the numerical solution are also shown. The new method gives second-and fourth-order accuracy in time and space, respectively. The algorithm uses five-point stencil to approximate the derivatives for the space discretization. The numerical experiments show that the proposed method improves the accuracy of the solution significantly.