J. Sanchez-Orea

Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

Transient and DC approximate expressions for diode circuits

In general terms, it is not possible to establish symbolic explicit analytic expressions of the operating point and transient analysis for circuits containing diodes modelled using an exponential function. Therefore, this work propose replacing the diode for an equivalent circuit obtained by using a power series and a Taylor series consecutively. Finally, we present a symbolic solution for some circuits that include diodes; resulting for the best case: for DC analysis a relative error of 1E-11 and for transient analysis a relative error ≤ 5E-4.

A Homotopy Continuation Approach for Testing a Basic Analog Circuit

The increase of complexity on integrated circuits has al so raised the demand for new testing methodologies capable to detect functional failures within circuits before they reach the market. Hence, this work proposes to explore the use of homotopy a s a tool for testing a basic analog circuit. The homotopy path is influenced by nonlinearities f rom the equilibrium equation of the circuit; this situation can be used to infer faults by det ecting changes on the homotopy path. The concept was explored using numerical simulation of a simple test circuit; then comparing results for the circuit with and without faults, obtaining modificat ions on the homotopy path like: the final point, number of iterations, and the number of turni ng points.

A generalization of the Bernoulli's method applied to brachistochrone-like problems

In this paper we study a generalization of the Johann Bernoullis solution of the brachistocrone 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 Eulers formalism for the calculus of variations, making it a handy and useful method for engineering applications. The provided examples will illustrate that this technique is equivalent to Eulers equation of the calculus of variations; for the particular case where one of the variables do not appear explicitly.

Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient.