It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials. In the multivariate case, a similar constructi...

Abstract: In this paper, a comparison between h ig h e r order schemes has been performed in terms of numerical accuracy. Four finite difference schemes, the e xp lic it fourth-order compact Pade scheme, the implicit fourth-order Pade scheme, flowfield dependent variation (FDV) meth o d a n d h igh order compact flowfie ld dependent variation (HOC-FDV) scheme are tes ted. The FDV scheme is used...

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original hi...

Ahsrruct: Section 1 describes the univariate situation in the case of non-normal Pade approximants and Cordellier’s extension of the famous five-star identity of Wynn. Section 2 repeats our definition of multivariate Pade approximants and proves a number of theorems that remain valid when going from the univariate to the multivariate case. These theorems and more new results given in Section 3....

We discuss the analytic continuation beyond μ/T ≃ 1 in QCD at nonzero T and μ by use of the Pade’ approximants. The slope of the critical line obtained in this way increases at large μ with respect to the second order Taylor result.In the hot phase Pade’ and Taylor approximants coincide, suggesting a very large, and possibly infinite, radius of convergence of the Taylor series in this thermodyn...

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

The nonlinear oscillator problem has extensive applications. In this paper, we examined the modified homotopy perturbation method to obtain the solution of the problem and to reduce the computational efforts. For the accuracy purpose the Laplace transform and Pade approximation have also been used. We construct the deformation equations by two components of the homotopy series, then by means of...

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the ot...