Simulating the shallow water equations by quasi-interpolation scheme based on a new transcendental RBF

Based on Wu-Schaback's quasi-interpolation for-mula, we use a new transcendental function (named RTH) as RBF which is proposed by Heidari [1] et al. The Degasperis-Procesi and Camassa-Holm equations are introduced firstly. Then the spatial derivatives are approached by the RTH quasi-interpolation and time discretization is applying the third order TVD. In numerical examples, we also use Multiquadric (MQ) function as RBF to approximate the solution of the equations, and compare it with RTH to show that the RTH has better accuracy