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- U. FILOBELLO-NINO, H. VAZQUEZ-LEAL, +5 authors J. CERVANTES-PEREZ
- 2013

In this paper, the perturbation method and Padé transformation are used to provide an approximate solution of elliptic integrals of the second kind and of complete integrals of the first kind. Besides, we used the obtained results to calculate an analytic expression for the period of a simple pendulum. The method has an acceptable accuracy for high values… (More)

- Héctor Vázquez-Leal, Uriel Filobello-Niño, +4 authors Anuar Ishak
- 2014

Nonlinear differential equations have applications in the modelling area for a broad variety of phenomena and physical processes; having applications for all areas in science and engineering. At the present time, the homotopy perturbation method HPM is amply used to solve in an approximate or exact manner such nonlinear differential equations. This method… (More)

- Héctor Vázquez-Leal, Arturo Sarmiento-Reyes, Yasir Khan, Uriel Filobello-Niño, Alejandro Díaz-Sánchez
- J. Applied Mathematics
- 2012

The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method RBHPM as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method… (More)

- Uriel Filobello-Nino, Hector Vazquez-Leal, +8 authors Jesus Huerta Chua
- SpringerPlus
- 2014

This article proposes Laplace Transform Homotopy Perturbation Method (LT-HPM) to find an approximate solution for the problem of an axisymmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and… (More)

- Uriel Filobello-Nino, Hector Vazquez-Leal, +9 authors Juan Cervantes-Perez
- SpringerPlus
- 2014

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures… (More)

- Hector Vazquez-Leal, Brahim Benhammouda, +6 authors Jesus Huerta-Chua
- SpringerPlus
- 2014

ABSTRACT
In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this… (More)

- H. Vazquez-Leal, V. M. Jimenez-Fernandez, +5 authors J. Huerta-Chua
- TheScientificWorldJournal
- 2014

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this… (More)

- Uriel Filobello-Nino, Hector Vazquez-Leal, +10 authors Leticia Cuellar-Hernandez
- SpringerPlus
- 2014

In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.

- Uriel Filobello-Niño, Héctor Vázquez-Leal, +10 authors Mario Gonzalez-Lee
- Neural Computing and Applications
- 2015

This article proposes the application of Laplace transform–homotopy perturbation method with variable coefficients, in order to find analytical approximate solutions for nonlinear differential equations with variable coefficients. As case study, we present the oxygen diffusion problem in a spherical cell including nonlinear Michaelis–Menten uptake kinetics.… (More)

- Uriel Filobello-Niño, Héctor Vázquez-Leal, +5 authors C. Hoyos-Reyes
- Applied Mathematics and Computation
- 2013

In this paper we study a generalization of the Johann Bernoulli's solution of the brachisto-crone problem. We will see that his method can be quickly extended in such a way that it can be used to solve other problems in a similar way using just elementary calculus methods. In addition, we will show that it is not necessary to know Euler's formalism for the… (More)