Abstract
A polynomial interpolation time-marching technique can efficiently provide balanced spectral accuracy in both the space and time dimensions for some PDEs. The Newton-form interpolation based on Fejér points has been successfully implemented to march the periodic Fourier pseudospectral solution in time. In this paper, this spectrally accurate time-stepping technique will be extended to solve some typical nonperiodic initial boundary value problems by the Chebyshev collocation spatial approximation. Both homogeneous Neumann and Dirichlet boundary conditions will be incorporated into the time-marching scheme. For the second order wave equation, besides more accurate timemarching, the new scheme numerically has anO(1/N 2) time step size limitation of stability, much larger thanO(1/N 4) stability limitation in conventional finitedifference time-stepping, Chebyshev space collocation methods.
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Luo, Y., Yedlin, M.J. Polynomial time-marching for nonperiodic boundary value problems. J Sci Comput 9, 123–136 (1994). https://doi.org/10.1007/BF01578383
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DOI: https://doi.org/10.1007/BF01578383