The program PEEI calculates a discrete, numerical and approximate solution of a generic differential analytical model (i.e. a system of partial differential equations).
Are exposed the mathematical bases of a computer program to numerically solve differential analytical models, i.e. systems of partial differential equations. Are described the analytical
properties of two well known models to approximate functions of a variable (the interpolating polynomial and the cubic spline) and new upper bounds for the errors of the second are
obtained. Are presented essential aspects of a curve in the multidimensional Euclidean space, in order to define the directional derivative of a function and to obtain an upper bound
for the absolute maximum value of a derivative definite on a curve. Is shown, for a point where intersect more curves, the expression of a partial derivative as a linear combination of
directional derivatives, and of it is deduced the optimum approximation when the values of these are approximate. Is formulated the expression of a generic differential analytical model,
highlighting in detail its arguments, identifying the principal impediment to the knowledge of an its exact solution in not knowing its partial derivatives, circumstantiating the context of
information contingently available, and showing how it can be calculated an its numerical solution solving an inherent system of not differential equations. Is exposed in detail the
algorithm that expresses a derivative of this system as a linear combination of his variables. Finally it is introduced, describing his use characteristics and essential actions, the program
PEEI that was realized, on the basis of the previous treatment, to calculate numerical solutions of differential analytical models.
The following prerequisites are required: Windows Installer 3.1 and .NET Framework 3.5 |