A recursive algorithm for Pade´-Hermite approximations
USSR Computational Mathematics and Mathematical Physics
Deciphering singularities by discrete methods
Mathematics of Computation
High-precision calculations of vortex sheet motion
Journal of Computational Physics
A study of singularity formation in the Kelvin-Helmholtz instability with surface tension
SIAM Journal on Applied Mathematics
Numerical study of bifurcations by analytic continuation of a function defined by a power series
SIAM Journal on Applied Mathematics
High-order differential approximants
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
We compute the singularities of the solution of the Birkhoff-Rott equation that governs the evolution of a planar periodic vortex sheet. Our approach uses the Taylor series obtained by Meiron et al. [J. Fluid Mech. 114 (1982) 283] for a flat sheet subject initially to a sinusoidal disturbance of amplitude a. The series is then summed by using various generalisations of the Padé method. We find approximate values for the location and type of the principal singularity as a ranges from zero to infinity. Finally, the results are used as a basis to guide the choice of methods of summing series arising from problems in fluid mechanics.