A numerically efficient Hamiltonian method for fractional wave equations
作者：
Highlights：
• A fractional multidimensional wave equation is studied numerically via a novel finite-difference method.
• The continuous system possesses positive energy invariants in the undamped case.
• The method has positive discrete energy functionals which are preserved in the undamped case.
• The existence and the uniqueness of the method are thoroughly established.
• The stability and the quadratic convergence of the technique are proved rigorously.
• The numerical simulations show the validity of the analytical results.
摘要
•A fractional multidimensional wave equation is studied numerically via a novel finite-difference method.•The continuous system possesses positive energy invariants in the undamped case.•The method has positive discrete energy functionals which are preserved in the undamped case.•The existence and the uniqueness of the method are thoroughly established.•The stability and the quadratic convergence of the technique are proved rigorously.•The numerical simulations show the validity of the analytical results.
论文关键词：Nonlinear fractional wave equation,Riesz space-fractional Laplacian,Discrete Hamiltonian method,Fractional centered differences,Discrete energy invariants,Stability and convergence analyses
论文评审过程：Received 27 March 2018, Accepted 3 June 2018, Available online 3 July 2018, Version of Record 3 July 2018.
论文官网地址：https://doi.org/10.1016/j.amc.2018.06.003
