A hybrid Fourier-Chebyshev method for partial differential equations

Rodrigo Platte, Anne Gelb

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We propose a pseudospectral hybrid algorithm to approximate the solution of partial differential equations (PDEs) with non-periodic boundary conditions. Most of the approximations are computed using Fourier expansions that can be efficiently obtained by fast Fourier transforms. To avoid the Gibbs phenomenon, super-Gaussian window functions are used in physical space. Near the boundaries, we use local polynomial approximations to correct the solution. We analyze the accuracy and eigenvalue stability of the method for several PDEs. The method compares favorably to traditional spectral methods, and numerical results indicate that for hyperbolic problems a time step restriction of O(1/N) is sufficient for stability.

Original languageEnglish (US)
Pages (from-to)244-264
Number of pages21
JournalJournal of Scientific Computing
Volume39
Issue number2
DOIs
StatePublished - May 2009

Keywords

  • Exponential convergence
  • Fourier spectral method
  • Hybrid methods
  • Non-periodic boundary conditions
  • Time-dependent pdes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A hybrid Fourier-Chebyshev method for partial differential equations'. Together they form a unique fingerprint.

Cite this