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

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：B-spline,Quasi-interpolation,DP equation,Finite difference,Numerical solution

论文评审过程：Received 26 April 2017, Revised 17 November 2017, Accepted 26 November 2017, Available online 28 December 2017, Version of Record 28 December 2017.

论文官网地址：https://doi.org/10.1016/j.amc.2017.11.058