Abstract
The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel. The scheme consists of Jacobi dual-Petrov Galerkin-Jacobi collocation method in space combined with Crank-Nicholson-leap-frog method in time such that at each time step only a sparse banded linear algebraic system needs to be solved. Numerical results are presented to show that the proposed numerical method is accurate and efficient for Korteweg-de Vries equations and other third-order nonlinear equations.
Citation
Ali H. Bhrawy. M. M. Al-Shomrani. "A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations." Abstr. Appl. Anal. 2012 1 - 16, 2012. https://doi.org/10.1155/2012/418943
Information