TITLE:
Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations
AUTHORS:
Edson Pindza, Eben Maré
KEYWORDS:
Fifth Order Korteweg-De Vries Equations; Discrete Singular Convolution; Exponential Time Discretization Method; Soliton Solutions; Conservation Laws
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.7,
December
12,
2013
ABSTRACT: A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) scheme and an exponential time integration scheme combined with the best rational approximations based on the Carathéodory-Fejér procedure for time discretization. We check several numerical results of our approach against available analytical solutions. In addition, we computed the conservation laws of the fKdV equation. We find that the DSC approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.