This paper is about a methodology to calculate all the components of the influence matrices of the curved boundary elements of three nodes in plane elasticity problems, using a semianalytical formulae and coordinate transformations, with which it is possible to savings of CPU time of the numerical integration used in these cases (Gauss-Legendre), maintaining its accuracy. To make the comparison of CPU times and precision of the results obtained by both techniques, numerical and semi-analytical subroutines were created using MAPLE symbolic-manipulation software. Among the results achieved is the reduction of computation times by 76%, 61% and 35% compared to the Gaussian numerical integration with four, six and eight integration points, respectively. That this technique successfully was used by the authors in the integration of matrices in the Finite Element Method (FEM).

In this work we present the numerical resolution of an initial and boundary value problem associated to one non-homogeneous parabolic EDP over a 2D domain with an isosceles triangle shape, using the explicit finite difference method (FDM) on an uniform mesh. The proposed numerical scheme combines a nine points stencil to approximate the solution in the nodes not adjacent to the boundary represented by the hypotenuse, and another one of eight points to approximate the solution in those that are adjacent to such boundary. By a standard analysis of FDM's it is demonstrated that the numerical scheme is stable, and this result is corroborated with numerical experiments.

In this paper, we present a qualitative study of the solutions of a mathematical model that is formulated to analyze the dynamical behavior of the exothermic and reversible chemical reaction, in a catalytic fixed bed reactor, adiabatically operated, and in presence of vanadium pentoxide. The model is a Cauchy problem for two coupled non-linear ordinary differential equations. These equations are coupled through the sulfur dioxide conversion, the temperature of the system (chemical reaction and chemical reactor) and its characteristic physicochemical parameters. We prove that the Cauchy problem has a unique solution (system orbits) for every initial condition that belongs to the domain for the directional field of the problem. We also show that the system orbits tend asymptotically to some stationary state located on an attracting manifold, embedded on the phase plane, when the time is large enough. These theoretical results allow us to describe the dynamic of a case given in the literature, in which it is reported the value of the physicochemical parameters, temperature ranges, and the reachable conversion levels in the industry. The dynamical behavior is as expected on the phase plane, and numerical results show that temperature changes of the system cause significantly changes in the conversion from to sulfur trioxide when time evolves.