Numerical Scheme to Dispersive Shallow Water Waves

Abstract

This paper studies dispersive shallow water waves modeled by Rosenau Korteweg-de Vries (KdV) Regularized long wave (RLW) equation or R-KdV-RLW equation that is considered with power law nonlinearity. The numerical algorithm is based on collocation finite element method with quintic B-splines. Test problems including the motion of solitary waves and shock waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable.