The novel family of transcendental Leal-functions with applications to science and engineering

Abstract

During the phenomena modelling process in the different areas of science and engineering is common to face nonlinear equations without exact solutions; thus, the need of employing numerical methods to obtain such solutions. Therefore, in order to provide new possibilities for the isolation of variables, we propose a novel family of transcendental functions with new algebraic properties including their integration and differentiation rules. Likewise, in order facilitate the numerical evaluation for every new family set of functions, a highly accurate series of approximations is proposed by employing analytical expressions in terms of known transcendental functions and polynomials combinations. By the use of known functions for the proposed approximations, makes possible the use of any programming language for their respective implementation. In this article, three interesting case studies are presented with applications on: coastal engineering, transmission lines span on electrical engineering, and the planar one-dimensional Bratu equation. Finally, based on the results from study cases, it can be concluded that Leal-functions will have relevant impact in all areas of physics and mathematics, by providing new tools to scientists and engineers for the proposal of new mathematical models and numerical/analytical analysis, design and implementation of new theories and technological innovations.

La didáctica del cálculo integral: el caso de los procedimientos de integración

“…Fuente: Vazquez et al (2020) Las funciones que se encuentran en la tabla 1 recientemente fueron publicadas, excepto Lambert W, que tiene su historia y que en años recientes su uso ha tomado mucha importancia en la ciencia y la ingeniería. Las funciones Leal también pertenecen al grupo de funciones trascendentes dado que poseen nuevas propiedades algebraicas que permiten realizar despejes, y de esta manera enriquecer el álgebra y la trigonometría.…”