A meshless symplectic algorithm for nonlinear wave equation using highly accurate RBFs quasi-interpolation

作者：Zhang, Shengliang^*; Yang, Yu; Yang, Hongqiang

来源：Applied Mathematics and Computation, 2017, 314: 110-120.

DOI：10.1016/j.amc.2017.07.010

• Radial basis functions
• High-order quasi-interpolation
• Symplectic integrator
• Hamiltonian PDEs

This study suggests a high-order meshless symplecitc algorithm for Hamiltonian wave equation by using highly accurate radial basis functions (RBFs) quasi-interpolation operator. The method does not require solving a resultant full matrix and possesses a high order accuracy compared with existing numerical methods. We also present a theoretical framework to show the conservativeness and convergence of the proposed symplectic method. As the numerical experiments shown, it not only offers a high order accuracy but also has a good property of long-time tracking capability.

• 出版日期2017-12-1
• 单位南京林业大学; 浙江外国语学院