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- Title
Space-time spectral collocation method for the one-dimensional sine- Gordon equation.
- Authors
Liu, Wenjie; Wu, Boying; Sun, Jiebao
- Abstract
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 L2-norm for the semidiscrete formulation. Numerical experiments show that our formulation have exponential rates of convergence in both space and time. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 670-690, 2015
- Subjects
SINE-Gordon equation; NONLINEAR analysis; TIME integration scheme; ORDINARY differential equations; DIFFERENTIAL equations
- Publication
Numerical Methods for Partial Differential Equations, 2015, Vol 31, Issue 3, p670
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.21910