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Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation

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  • Xiaoquan Ding
  • Qing-Jiang Meng
  • Li-Ping Yin

Abstract

We present a discrete-time orthogonal spline collocation scheme for the one-dimensional sine-Gordon equation. This scheme uses Hermite basis functions to approximate the solution throughout the spatial domain on each time level. The convergence rate with order in norm and stability of the scheme are proved. Numerical results are presented and compared with analytical solutions to confirm the accuracy of the presented scheme.

Suggested Citation

  • Xiaoquan Ding & Qing-Jiang Meng & Li-Ping Yin, 2015. "Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, December.
    • Handle: RePEc:hin:jnddns:206264
    DOI: 10.1155/2015/206264
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