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.

DOI: 10.4236/jamp.2015.39144                

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Chicurel-Uziel, E. (2007) Dirac Delta Representation by Exact Parametric Equations. Application to Impulsive Vibration Systems. Journal of Sound and Vibration, 305, 134-150. http://dx.doi.org/10.1016/j.jsv.2007.03.087
[2]	Chicurel-Uziel, E. and Godínez-Rojano, F.A. (2013) Parametric Dirac Delta to Simplify the Solution of Linear and Nonlinear Problems with an Impulsive Forcing Function. Journal of Applied Mathematics and Physics, 1, 16-25. http://dx.doi.org/10.4236/jamp.2013.17003
[3]	Greenberg, M.D. (1998) Advanced Engineering Mathematics. Prentice Hall, Upper Saddle River, 269.
[4]	Stakgold, I. (1998) Green’s Functions and Boundary Value Problems. Wiley, New York, 57-58.
[5]	Butkov, E. (1973) Mathematical Physics. Addison Wesley, Reading.
[6]	Hoskins, R.F. (1979) Generalized Functions. Ellis Horwood Ltd., Wiley & Sons, Chichester, 42.
[7]	Asmar, N.H. (2000) Partial Differential Equations and Boundary Value Problems. Pearson Prentice Hall, Prentice Hall, 146.
[8]	Haberman, R. (2004) Applied Partial Differential Equations. Pearson Prentice Hall, Upper Saddle River.
[9]	Zauderer, E. (1989) Partial Differential Equations of Applied Mathematics. John Wiley & Sons, Hoboken, 430.