Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis-Procesi equation

In this paper, the Degasperis-Procesi (DP) equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form: u−P. Based on the equivalent formulation of DP equation, a new numerical method is presented. The multi-quadric (MQ) quasi-interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order TVD method is used to approximate the time derivative. Several examples are presented to demonstrate the effectiveness of the proposed method.