Numerical solution of the Degasperis–Procesi equation by the cubic B-spline quasi-interpolation method

In this paper, a numerical scheme is presented to solve the non-dissipative Degasperis–Procesi equation based on the u-p formulation. The cubic B-spline quasi-interpolation coupled with the finite difference method is applied to approximate the spatial derivatives and an optimal third order TVD Runge–Kutta method to estimate the time derivative of the dependent variable. The accuracy and effectiveness of the proposed method are validated by six classical problems. Numerical results indicate that the proposed scheme is simple, easy to implement with high accuracy.