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Interpolating discrete advection–diffusion propagators at Leja sequences

Journal of Computational and Applied Mathematics, ISSN: 0377-0427, Vol: 172, Issue: 1, Page: 79-99
2004
  • 52
    Citations
  • 0
    Usage
  • 17
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    52
    • Citation Indexes
      52
  • Captures
    17

Article Description

We propose and analyze the ReLPM (Real Leja Points Method) for evaluating the propagator ϕ (Δ tB ) v via matrix interpolation polynomials at spectral Leja sequences. Here B is the large, sparse, nonsymmetric matrix arising from stable 2D or 3D finite-difference discretization of linear advection–diffusion equations, and ϕ ( z ) is the entire function ϕ ( z )=(e z −1)/ z. The corresponding stiff differential system ẏ(t)=By(t)+g,y(0)=y0, is solved by the exact time marching scheme y i+1 = y i +Δ t i ϕ (Δ t i B )( B y i + g ), i =0,1,…, where the time-step is controlled simply via the variation percentage of the solution, and can be large. Numerical tests show substantial speed-ups (up to one order of magnitude) with respect to a classical variable step-size Crank–Nicolson solver.

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