Journal of Applied Mathematics and Physics, 2015, 3, 1168-1177
Published Online September 2015 in SciRes. http://www.scirp.org/journal/jamp
http://dx.doi.org/10.4236/jamp.2015.39144
How to cite this paper: Chicurel-Uziel, E.J. and Godínez, F.A. (2015) Parametrization to Improve the Solution Accuracy of
Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function. Journal of Applied Mathematics and Physics, 3,
1168-1177. http://dx.doi.org/10.4236/jamp.2015.39144
Parametrization to Improve the Solution
Accuracy of Problems Involving the
Bi-Dimensional Dirac Delta in the
Forcing Function
Enrique J. Chicurel-Uziel, Francisco A. Godínez
Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F., México
Email: ecu@pumas.ii.unam.mx , fgodinezr@gmail.com
Received 25 July 2015; accepted 20 September 2015; published 23 September 2015
Copyright © 2015 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
The representation of the Dirac delta, obtained by differentiating the parametric equation of the
unit step with a riser, is used to solve two examples referring to problems of a different physical
nature, each with the product of two deltas as a forcing function. Each problem was solved by an
entirely different procedure. In comparison with non-parametric solutions, the present solutions
are both more accurate and truer representations of the physics involved.
Keywords
Dirac Delta, Partial Differential Equations, Parametric Representation
1. Introduction
One purpose of this paper is to emphasize the fact that the parametric delta is an exact representation, i.e., its
value is zero everywhere except at one single point, and at that point its value is infinity. Another purpose is to
illustrate the use and the effect of the parametric delta relating to two-dimensional domains, in space-time or in
space-space; in these two cases, a product of deltas is involved, of course. Still another purpose is to present a
problem example in which the operator action of the parametric delta facilitates the solution.
According to distribution theory, the Dirac delta is the result of differentiating the Heaviside unit step. The
particular parametrization presented in [1] permits this differentiation to be carried out by means of elementary
calculus and the resulting pair of parametric equations is exact and closed.
It is well to keep in mind that the parametric equations of the delta confirm that its area has unit value, that