Abstract:
In this paper a Petrov-Galerkin method is used to derive a scheme for the K(2,2) equation, where we have chosen cubic B-splines as test functions and linear functions as trial functions. Product approximation technique is applied for the nonlinear terms. A Crank-Nicolson Scheme is used to discretize in time. A nonlinear penta-diagonal system is obtained and we solve this system by Newton’s method and by a linearization technique. Accuracy and stability of the scheme have been investigated. The single compacton solution and the conserved quantities are used to assess the accuracy of the scheme. The interaction of two compactons are displayed and the numerical results have shown that these compacton solutions exhibits true solution.
Page(s):
21-26
DOI:
DOI not available
Published:
Journal: Proceedings of Pakistan Academy of Sciences, Volume: 44, Issue: 1, Year: 2007