Space-Time Spectral Collocation Method for the One-Dimensional Sine-Gordon Equation

作者：Liu, Wenjie; Wu, Boying; Sun, Jiebao^*

来源：Numerical Methods for Partial Differential Equations, 2015, 31(3): 670-690.

DOI：10.1002/num.21910

• sine-Gordon equation
• space-time spectral collocation method
• error estimates

In this article, we introduce a new space-time spectral collocation method for solving the one-dimensional sine-Gordon equation. We apply a spectral collocation method for discretizing spatial derivatives, and then use the spectral collocation method for the time integration of the resulting nonlinear second-order system of ordinary differential equations (ODE). Our formulation has high-order accurate in both space and time. Optimal a priori error bounds are derived in the L-2-norm for the semidiscrete formulation. Numerical experiments show that our formulation have exponential rates of convergence in both space and time.

• 出版日期2015-5
• 单位哈尔滨工业大学