Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Barycentric rational interpolation with asymptotically monitored poles
Numerical Algorithms
Computers & Mathematics with Applications
Recent advances in linear barycentric rational interpolation
Journal of Computational and Applied Mathematics
Hi-index | 0.01 |
A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Pade´ approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to $[-1,1]$.