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.
Highlights
Where ukx ku xk, and are real numbers
We investigate the convergence of the Discrete singular convolution (DSC) method with respect to the number of the grid points N and the DSC bandwidth M as we did in the case of one soliton solutions
We studied the application of the combined DSC scheme in space discretization and the ETDRK4 for time discretization to solve the SK and KK equations
Summary
Where ukx ku xk , and are real numbers. This class includes the well-known Lax [1], Sawada-Kotera (SK) [2], Kaup-Kupershmidt (KK) [3] and Ito [4] equations. We propose a discrete singular convolution method to solve fifth order Korteweg-de Vries equations. Discrete singular convolution (DSC) methods belong to the family of local spectral (LS) methods They were proposed by Wei [8] as a potential approach for. Pindza and Maré [17] utilized a combined fourth order exponential time differencing of Adams type and the DSC method to solve the generalized Kortewegde Vries.
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