Abstract:
This paper is devoted to create new exact and numerical solutions of the generalized
Korteweg-de Vries (GKdV) equation with ansatz method and Galerkin finite element
method based on cubic B-splines over finite elements. Propagation of single solitary
wave is investigated to show the efficiency and applicability of the proposed methods.
The performance of the numerical algorithm is proved by computing L2 and L∞ error
norms. Also, three invariants I1, I2, and I3 have been calculated to determine the
conservation properties of the presented algorithm. The obtained numerical solutions
are compared with some earlier studies for similar parameters. This comparison
clearly shows that the obtained results are better than some earlier results and
they are found to be in good agreement with exact solutions. Additionally, a linear
stability analysis based on Von Neumann’s theory is surveyed and indicated that
our method is unconditionally stable.
