Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

A reduced order modeling method based on a system description in terms of orthonormal Laguerre functions, together with a Krylov subspace decomposition technique is presented. The link with Padé approximation, the block Arnoldi process and singular value decomposition (SVD) leads to a simple and stable implementation of the algorithm. Novel features of the approach include the determination of ...

We present an asymptotic Padé-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass m A = 100 GeV , into two gluons. All but one of these coefficients are shown to be determined for arbitrary m A from the known 3-loop-order rate by renormalization group methods. A...

We present a numerical study of the resolution power of Padé Approximations to the Z-transform, compared to the Fourier transform. As signals are represented as isolated poles of the Padé Approximant to the Z-transform, resolution depends on the relative position of signal poles in the complex plane i.e. not only the difference in frequency (separation in angular position) but also the differen...

A novel application of the Padé approximation is proposed in which the Padé approximant is used as an interpolation for the small and large coupling behaviors of a physical system, resulting in a prediction of the behavior of the system at intermediate couplings. This method is applied to quarkonium systems and reasonable values for the c and b quark masses are obtained. PACS: 11.15.Me, 11.15.T...

Boyd shows in [3] that for a function with singularities in the imaginary plane, the Gegenbauer expansion of the function may have Runge-type oscillations so large that all hope of convergence for the method is lost. We consider the use of Padé-Gegenbauer interpolants to resolve these oscillations. We describe a fast interpolation-based reconstruction for computing the Padé-Gegenbauer approxima...

The contribution of the α3 single electron-loop vacuum-polarization diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently by two methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Padé approximation method. High numerical precision of these calculations enables us to examine the accuracy of the Monte-Ca...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...

In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Padé approximants converges uniformly in compact subsets of the ball omitting poles of f . There is also apparently a cruder version of the conjecture due to Padé himself, going back to the early twentieth century. We show here that for carefully chosen q on the unit cir...