Numerical algorithms for solutions of Korteweg–de Vries equation
✍ Scribed by Alper Korkmaz
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 243 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0749-159X
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## Abstract A numerical method for solving the coupled Korteweg‐de Vries (CKdV) equation based on the collocation method with quintic B‐spline finite elements is set up to simulate the solution of CKdV equation. Invariants and error norms are studied wherever possible to determine the conservation
We study the asymptotic behavior for large time of solutions to the Cauchy problem for the generalized Korteweg de Vries (gKdV) equation u t + ( |u| \&1 u) x + 1 3 u xxx =0, where x, t # R when the initial data are small enough. If the power \ of the nonlinearity is greater than 3 then the solution
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