Space‐time spectral collocation method for the one‐dimensional sine‐Gordon equation |
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Authors: | Wenjie Liu Boying Wu Jiebao Sun |
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Affiliation: | Department of Mathematics, Harbin Institute of Technology, Harbin, People'sRepublic of China |
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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 |
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Keywords: | sine‐Gordon equation space‐time spectral collocation method error estimates |
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