The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials

Abstract In this paper, we introduce the Galerkin method using a new basis of smooth piecewise cubic polynomials for the one-dimensional nonlinear KdV equation. The stability analysis shows that the present method is unconditionally stable in L 2 -norm. Numerical experiments show that the proposed method preserves the conservation laws and is effective for simulating the motions and the interactions of solitary waves.