Conservative multiquadric quasi-interpolation method for Hamiltonian wave equations

Hamiltonian PDEs have some invariant quantities such as energy and momentum, etc., which should be well conserved with the numerical integration. In this paper we concentrate on the nonlinear wave equation. We study how a space discretization by using multiquadric quasi-interpolation method makes the space discretized system also possess some invariants which are good approximation of the continuous energy. Then, appropriate symplectic scheme is employed for the integration of the semi-discretized system. Theoretical results show that the proposed method has not only high order accuracy but also good properties of long-time tracking capability. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.