In this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...

Although general order multivariate Padé approximants were introduced some decades ago, very few explicit formulas for special functions have been given. We explicitly construct some general order multivariate Padé approximants to the class of so-called pseudo-multivariate functions, using the Padé approximants to their univariate versions. We also prove that the constructed approximants inheri...

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...

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, 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...

The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solut...

in this paper, the differential transform method and padé approximation (dtm-padé) is applied to obtain the approximate analytical solutions of the mhd flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. the similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...

The paper reviews the relation between Padé-type approximants of a power series and interpolatory quadrature formulas with free nodes, and that between Padé approximants and Gaussian quadrature methods. Quadrature methods are well-known. They are used for obtaining an approximate value of a definite integral, and are described in any book of numerical analysis. In this talk, we will show that P...

The classical Lanczos process can be used to efficiently generate Padé approximants of the transfer function of a given single-input single-output time-invariant linear dynamical system. Unfortunately, in general, the resulting reduced-order models based on Padé approximation do not preserve the stability, and possibly passivity, of the original linear dynamical system. In this paper, we descri...