Héctor Vázquez-Leal

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The purpose of this study is to introduce an efficient iterated homotopy perturbation transform method (IHPTM) for solving a mathematical model of HIV infection of CD4+ T cells. The equations are Laplace transformed, and the nonlinear terms are represented by He’s polynomials. The solutions are obtained in the form of rapidly convergent series with(More)
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)
The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method RHPM as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We(More)
The continuous scaling for fabrication technologies of electronic circuits demands the design of new and improved simulation techniques for integrated circuits. Therefore, this work shows a new double bounded polynomial homotopy based on a polynomial formulation with four solution lines separated by a fixed distance. The new homotopy scheme presents a(More)
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)
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)
A homotopy method for obtaining DC solutions of nonlinear circuits is proposed. The homotopy method is called double-bounded homotopy and it is used to find multiple DC solutions. This method presents a novel stop criterion which is based on the property of tracing a double bounded trajectory. The main properties of the homotopy are explained by using the(More)
We present a signal processing system with virtual instrumentation of a MEMS sensor to detect magnetic flux density for biomedical applications. This system consists of a magnetic field sensor, electronic components implemented on a printed circuit board (PCB), a data acquisition (DAQ) card, and a virtual instrument. It allows the development of a(More)
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the(More)