We apply the method of operator splitting on the generalized Korteweg-de Vries (KdV) equation u t + f (u) x + εu xxx = 0, by solving the nonlinear conservation law u t + f (u) x = 0 and the linear dispersive equation u t + εu xxx = 0 sequentially. We prove that if the approximation obtained by opera
Separation method for solving the generalized Korteweg–de Vries equation
✍ Scribed by A. Zerarka; V.G. Foester
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 427 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1007-5704
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✦ Synopsis
A separation method is introduced within the context of dynamical system for solving the non-linear Korteweg-de Vries equation (KdV). Best efficiency is obtained for the number of iterations (n 6 8). Comparisons with the solutions of the quintic spline, finite difference, moving mesh and pseudo-spectral are presented.
📜 SIMILAR VOLUMES
The Korteweg-de Vries equation is numerically solved by using a new algorithm based on the quintic sphne approximation. An iterative scheme having 0(k2 + kh2) accuracy and five-band constant coefficients system of equations is devised. The stability of the proposed scheme is discussed. Comparisons
The generalized KdV-Burgers equation u t +(δu xx +g(u)) x -νu xx +γ u = f (x), δ, ν > 0, γ ≥ 0, is considered in this paper. Using the parabolic regularization technique we prove local and global solvability in H 2 (R) of the Cauchy problem for this equation. Several regularity properties of the app