We show that a simple and straightforward rational approximation to the Thomas– Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Padé approximants are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas–Fermi equation for isolated atoms and for atoms in strong magnetic fields.

In this note we consider the stability preserving properties of diagonal Padé approximations to the matrix exponential. We show that while diagonal Padé approximations preserve quadratic stability when going from continuous-time to discrete-time, the converse is not true. We discuss the implications of this result for discretizing switched linear systems. We also show that for continuous-time s...

In this paper, a technique to approximate a class of passive delay systems by a bond graph model is investigated. This method is designed to preserve the passivity of the initial model. Through interconnections of passive elementary blocks (passivity is stable under interconnections), a finite dimensional passive approximant is constructed. This finite dimensional model, if need be, is reduced ...

In this article an analytical technique, namely the homotopy analysis method (HAM), is applied to solve the momentum and energy equations in the case of a two-dimensional incompressible flow passing over a wedge. The trail and error method and Padé approximation strategies have been used to obtain the constant coefficients in the approximated solution. The effects of the polynomial terms of HAM...

In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé approximants. This modified homotopy perturbation method (MHPM) utilizes an alternative framework to capture the periodic behavior of the solution, which is characteristic of oscillator equations, and to give a ...

We study AAK-type meromorphic approximants to functions of the form F (z) = ∫ dλ(t ) z − t +R(z), where R is a rational function and λ is a complex measure with compact regular support included in (−1,1), whose argument has bounded variation on the support. The approximation is understood in Lp -norm of the unit circle, p ≥ 2. We dwell on the fact that the denominators of such approximants sati...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

We classify all integer squares (and, more generally, q-th powers for certain values of q) whose ternary expansions contain at most three digits. Our results follow from Padé approximants to the binomial function, considered 3-adically. –Dedicated to the memory of John Selfridge.

This is a continuation of our earlier paper [PT3]. We consider here operator-valued functions (or infinite matrix functions) on the unit circle T and study the problem of approximation by bounded analytic operator functions. We discuss thematic and canonical factorizations of operator functions and study badly approximable and very badly approximable operator functions. We obtain algebraic and ...

Large and sparse rational eigenproblems where the rational term is of low rank k arise in vibrations of fluid–solid structures and of plates with elastically attached loads. Exploiting model order reduction techniques, namely the Padé approximation via block Lanczos method, problems of this type can be reduced to k–dimensional rational eigenproblems which can be solved efficiently by safeguarde...