In this paper, an integration of a symbolic power series method - Padé approximation technique (PS - Padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. As both boundary conditions tended to infinity, the combination of series solut...

A more interesting use of Padé approximation is “two-point Padé approximation” or Padé interpolation in which a Padé approximant for f(x) is constructed from two truncated Taylor series: one for when x is very small and one is for when x is very large. The Padé approximant in this method interpolates between the values at which f(x) is known. This method is directly applicable to perturbation t...

For computing Padé approximants, we present presumably stable recursive algorithms that follow two adjacent rows of the Padé table and generalize the well-known classical Levinson and Schur recurrences to the case of a nonnormal Padé table. Singular blocks in the table are crossed by look-ahead steps. Ill-conditioned Padé approximants are skipped also. If the size of these lookahead steps is bo...

We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infinite dimensional linear subs...

We give a short introduction to Padé approximation (rational approximation to a function with close contact at one point) and to Hermite-Padé approximation (simultaneous rational approximation to several functions with close contact at one point) and show how orthogonality plays a crucial role. We give some insight into how logarithmic potential theory helps in describing the asymptotic behavio...

Kronrod's procedure is a method for estimating the error in Gaussian quadrature methods. Padé approximants are formal Gaussian quadrature formulas. In a previous paper, Kronrod's method was used to obtain .estimates of the error in Padé approximation. Using a new interpretation of this procedure and three different expressions of the error of Padé approximants, extensions of the method are obta...

In this paper the discretization of switched and non-switched linear positive systems using Padé approximations is considered. We show: 1) diagonal Padé approximations preserve both linear and quadratic co-positive Lyapunov functions; 2) positivity need not be preserved even for arbitrarily small sampling time for certain Padé approximations. Sufficient conditions on the Padé approximations are...

For univariate functions the Kronecker theorem, stating the equivalence between the existence of an infinite block in the table of Padé approximants and the approximated function f being rational, is well-known. In [Lubi88] Lubinsky proved that if f is not rational, then its Padé table is normal almost everywhere: for an at most countable set of points the Taylor series expansion of f is such t...

Abstract. A matrix triangularization interpretation is given for the recursive algorithms computing the Padé approximants along a certain path in the Padé table, which makes it possible to unify all known algorithms in this field [5], [6]. For the normal Padé table, all these results carry over to the matrix Padé problem in a straightforward way. Additional features, resulting from the noncommu...

In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II andmodified Padé-II equation.Themapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined PadéII and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, r...