A NOTE ON QUADRATIC RICCATI DIFFERENTIAL EQUATION USING PADÉ APPROXIMANT

  • Pedro Pablo Cárdenas Alzate Department of Mathematics, Universidad Tecnológica de Pereira and GEDNOL, Colombia
  • Álvaro Andrés Quintero Orrego InstituciónUniversitaria EAM, Colombia
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.

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References

Padé, H. Sur la représentation approchée d’une fonction par des fractions rationnelles, Annales scientifiques de l’E.N.S. 3 série, tome 9 (1892), 3-93 DOI: https://doi.org/10.24033/asens.378

Padé, H. Mémoire sur les développements en fractions continues de la function exponentielle, pouvant servir d’introduction à la théorie des fractions continues algébraiques, Annales scientifiques de l’ENS. 3 série, tome 16 (1899), 395-426.

Padé, H. Recherches sur la convergence des développements en fractions continues d’une certaine catégorie des fonctions. Annales scientifiques de l’ENS, 3 série, tome 24 (1907), 341-400.

Shatnawi, M.T. Solving boundary layer problems by residual power series method. Journal of Mathematics Research, 8 (2016), 68-73.

Cárdenas, P. An iterative method for solving two special cases of Lane-Emden type equations. American Journal of Computational Mathematics, 4(2014), 242-253.

Vasquez, L et al. Direct application of Padé approximant for solving nonlinear differential equations. Springer Plus, 3(2014), 563-574.

Published
2020-06-20
How to Cite
Alzate, P. P. C., & Orrego, Álvaro A. Q. (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