ZHAN Jie-min, LI Yok-sheung, DONG Zhi. Chebyshev Finite Spectral Method With Extended Moving Grids[J]. Applied Mathematics and Mechanics, 2011, 32(3): 365-374. doi: 10.3879/j.issn.1000-0887.2011.03.012
Citation: ZHAN Jie-min, LI Yok-sheung, DONG Zhi. Chebyshev Finite Spectral Method With Extended Moving Grids[J]. Applied Mathematics and Mechanics, 2011, 32(3): 365-374. doi: 10.3879/j.issn.1000-0887.2011.03.012

Chebyshev Finite Spectral Method With Extended Moving Grids

doi: 10.3879/j.issn.1000-0887.2011.03.012
  • Received Date: 2010-01-25
  • Rev Recd Date: 1900-12-30
  • Publish Date: 2011-03-15
  • A Chebyshev finite spectral method on non-uniform mesh was proposed.An equidistribution scheme for two types of extended moving grids was proposed for grid generation.One type of grid was designed to provide better resolution for wave surface.The other type was for highly variable gradients.The method was of high-order accuracy because of the use of Chebyshev polynomial as the basis function.The polynomial was used to interpolate values between the two non-uniform meshes from the previous time step to the current time step.To attain high accuracy in time discretization,the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used.To avoid numerical oscillations caused by the dispersion term in the KdV equation,a numerical technique on non-uniform mesh was introduced to improve the numerical stability.The proposed numerical scheme was validated by applications to the Burgers equation (nonlinear convection-diffusion problem) and KdV equation (single solitary and 2-solitary wave problems),where analytical solutions were available for comparison.Numerical results agree very well with the corresponding analytical solutions in all cases.
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