ISSN: 2454-1907 International Journal of Engineering Technologies and Management Research June 2020, Vol 7(06), 117 – 124 DOI: https://doi.org/10.29121/ijetmr.v7.i6.2020.697 © 2020 The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 117 A NOTE ON QUADRATIC RICCATI DIFFERENTIAL EQUATION USING PADÉ APPROXIMANT Pedro Pablo Cárdenas Alzate *1 , Álvaro Andrés Quintero Orrego 2 *1 Department of Mathematics, Universidad Tecnológica de Pereira and GEDNOL, Colombia 2 Institución Universitaria EAM, Colombia DOI: https://doi.org/10.29121/ijetmr.v7.i6.2020.697 Article Citation: Pedro Pablo Cárdenas Alzate, and Álvaro Andrés Quintero Orrego. (2020). A NOTE ON QUADRATIC RICCATI DIFFERENTIAL EQUATION USING PADÉ APPROXIMANT. International Journal of Engineering Technologies and Management Research, 7(6), 117 – 124. https://doi.org/10.29121/ijetmr.v7 .i6.2020.697 Published Date: 20 June 2020 Keywords: Padé Approximant Quadratic Riccati Semi-Analytical Method Normal Padé table ABSTRACT Semi-analytical methods for solving non-linear models require an initial approach to determine the solutions sought and the calculation of one or more fitting parameters. When the initial approach is chosen correctly, the results can be very precise, but not there is a general method for choosing such an initial approach. In this paper, it is suggested to use directly the serial solution of a non-linear model to find Padé's approximation with highly efficient results. 1. INTRODUCTION The resolution of non-linear differential equations is a very important problem in the sciences in general since many phenomena are modeled using this type of equation. It is also true that in most cases, it is not possible to find analytical solutions to such models and therefore knowledge of efficient numerical methods to approximate them is essential. Thus, there are several semi-analytical methods that allow us to approximate the solutions numerically, such as the Adomian decomposition method, the differential transformation and the Padé method [1]. For this reason, the Padé Method is widely used in computer calculations. This method has proven to be very useful in obtaining quantitative information about the solution of many interesting problems in physics-mathematics and engineering. The applications of Padé's main approaches are divided into two classes: • The provision of efficient rational approaches to special mathematical functions • The acquisition of quantitative information about a function for which you only have qualitative information and coefficients in power series. The Padé approximations, obtained as the quotient of two polynomials from Taylor's coefficients of series expansion, are the basis of many non-linear methods and have close connections with the famous ɛ-algorithm, continuous fractions and orthogonal polynomials. The Padé approximations are the non-linear counterpart of the first-order Taylor series expansions used in linear methods.