LAUSR

Abstract The nonlinear Degasperis-Procesi (DP) equation allows shock wave solutions and possesses bi-Hamiltonian properties. Considering both of the two properties, we introduce a numerical scheme which involves three key features. First, a stable moving knots strategy is introduced to simulate the shock waves with less knots. Second, the moving knots equation together with the DP equation are simulated using the meshless multi-quadric (MQ) quasi-interpolation method, which allows scattered data approximation. Third, the proposed moving knots meshless scheme preserves the conservation laws. Both theoretical analysis and numerical examples demonstrate that the algorithm saves the computational time, improves the accuracy, and possesses a long-time tracking capability.