The purpose of this study is to introduce a modification of the homotopy perturbation method using Laplace transform and Padé approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations. Two test examples are given; the coupled nonlinear system of Burger equations and the coupled nonlinear system in one dimensional thermoelasticity. The results o...

Given non-collinear points a1, a2, a3, there is a unique compact ∆ ⊂ C that has minimal logarithmic capacity among all continua joining a1, a2, and a3. For a complex-valued non-vanishing Dinicontinuous function h on∆, we define fh (z) := 1 πi ∫ ∆ h(t ) t − z d t w+(t ) ,

Using asymptotic Padé approximant methods, we have calculated the O(αs) contribution to the Standard-Model H → gg decay rate. This process is of particular interest because of the slow convergence evident from the known terms of its QCD series. The O(αs) term is expressed as a 3rd degree polynomial in L ≡ ln (

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 thermodynam...

Based on a “monotonicity” analogue of the l’Hospital Rule, monotonicity properties of the relative error are established for a Padé approximation of Mills’ ratio.

We describe some applications of the Euclidean algorithm in modern computational problems like Padé approximation, iterative solution of linear systems, eigenvalue problems, orthogonal polynomials, coding theory etc.

Padé-improvement of four-loop β-functions in massive φ 4 scalar field theory is shown to predict the known five-loop contribution with astonishing (0.2%) accuracy, supporting the applicability of Padé-summations for approximating all-orders MS QCD β-functions, as suggested by Ellis, Karliner, and Samuel. Surprisingly, the most general set of [2|2] approximants consistent with known two-, three-...