Symplectic Schemes for Quasilinear Wave Equations of Klein-Gordon and Sine-Gordon Type (Journal of Computational Mathematics, 2001)
A class of finite difference methods of first- and second-order accuracy for the computation of solutions to the quasilinear wave equations is presented. These difference methods are constructed based on the symplectic schemes to the infinite-dimensional Hamiltonian system. Numerical experiments are presented to demonstrate the superior performance of these methods.
Keywords: Symplectic integration; Sine-Gordon equations; Finite difference method.