We investigate the asymptotic behavior for type II Hermite-Padé approximation to two functions, where each function has two branch points and the pairs of branch points are separated. We give a classification of the cases such that the limiting counting measures for the poles of the Hermite-Padé approximants are described by an algebraic function h of order 3 and genus 0. This situation gives r...

This paper presents a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric and may be considered a more general version of the standard compact (Padé) schemes discussed by Lele. They are different from the standard Padé schemes, in that the first and second derivatives are evaluated simultaneously. For the same ste...

A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than the twosided Padé approximants and modified Padé approximants, including these as particular cases. Being more general, the self-similar root approximants gu...

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

Diagonal cubic Hermite-Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas and differential equations are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and it is also shown that these generalized Padé-type approximations can be used to asymptotically minimiz...

Wide-angle scalar beam propagation methods (BPMs) for effective modelling of optical propagation in three-dimensional (3D) waveguides are usually limited to the low-order-accurate Padé(1,1) approximant. Presented is a 3D wide-angle scalar BPM based on higher-order Padé approximant operators which is factored into a series of simpler first-order Padé(1,1) approximants. This results in a multiste...

For k + 1 power series a0(z), . . . , ak(z), we present a new iterative, look-ahead algorithm for numerically computing Padé-Hermite systems and simultaneous Padé systems along a diagonal of the associated Padé tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are wellconditioned. The operati...