Fronts, relaxation oscillations, and period doubling in solid fuel combustion
Journal of Computational Physics
On the use of spectral methods for the numerical solution of stiff problems
Computer Methods in Applied Mechanics and Engineering
Spectral integration and two-point boundary value problems
SIAM Journal on Numerical Analysis
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
Roundoff error in computing derivatives using the Chebyshev differentiation matrix
Journal of Computational Physics
The barycentric weights of rational interpolation with prescribed poles
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Exponential convergence of a linear rational interpolant between transformed Chebyshev points
Mathematics of Computation
Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
SIAM Journal on Numerical Analysis
Spectral methods in MatLab
The linear rational collocation method
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Adaptive point shifts in rational approximation with optimized denominator
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Journal of Computational Physics
A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points
SIAM Journal on Scientific Computing
Barycentric rational interpolation with no poles and high rates of approximation
Numerische Mathematik
Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods
ACM Transactions on Mathematical Software (TOMS)
Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium
Journal of Computational Physics
Recent advances in linear barycentric rational interpolation
Journal of Computational and Applied Mathematics
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
Journal of Computational Physics
Hi-index | 31.46 |
This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.