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

•Use the cubic B-spline quasi-interpolation method to solve the Degasperis–Procesi equation.•Use the cubic B-spline quasi-interpolation scheme to approximate the spatial derivatives.•Use an optimal third order TVD Runge–Kutta method to estimate the temporal derivative.•The proposed method can capture the shock accurately.•There is no need to select the parameter.