A meshless symplectic algorithm for nonlinear wave equation using highly accurate RBFs quasi-interpolation
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摘要
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.
论文关键词:Radial basis functions,High-order quasi-interpolation,Symplectic integrator,Hamiltonian PDEs
论文评审过程:Received 22 August 2016, Revised 26 April 2017, Accepted 2 July 2017, Available online 17 July 2017, Version of Record 17 July 2017.
论文官网地址:https://doi.org/10.1016/j.amc.2017.07.010