Using a complete orthonormal system of functions in L2(-∞, ∞) a Fourier-Galerkin spectral technique is developed for computing of the localized solutions of equations with cubic nonlinearity. A formula expressing the triple product into series in the system is derived. Iterative algorithm implementing the spectral method is developed and tested on the soliton problem for the cubic Boussinesq equation. Solution is obtained and shown to compare quantitatively very well to the known analytical one. The issues of convergence rate and truncation error are discussed.
|Number of pages||15|
|Journal||Journal of Computational Analysis and Applications|
|Publication status||Published - 2002|
- Cubic Boussinesq equation
- Galerkin approximation
- Localized solutions
- Spectral methods