Resumen
En este artículo se propone una expresión compacta y precisa de la función de Dawson, la cual es invertible e integrable. Se observa que el error relativo máximo que se encuentra empleando la aproximación aquí propuesta es del 2.5%. Por consiguiente, se hace notar que la aproximación a la integral de la función de Dawson, que se expresa solo en términos de funciones elementales, tiene un error absoluto máximo de 7 × 10-3. A manera de ejemplo, se aplicará la aproximación aquí propuesta a un problema no-clásico de conducción de calor para obtener una solución aproximada, compacta y precisa.
Citas
Belser, W. (1999) Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations. New York: Springer.
Boyd, J.P (2008). Evaluating of Dawson's integral by solving its differential equation using orthogonal rational Chebyshev functions. Applied Mathematics and Computation, 204, 914-919.
Briozzo, A.C., Tarzia, D.A. (2010). Exact solutions for nonclassical Stefan problems. International Journal of Differential Equations, 2010, 1-19 Article ID 868059. doi: 10.1155/2010/868059.
Cody, W.J., Kathleen A. Paciorek, K.A. & Thacher, H.C. (1970) Chebyshev approximations for Dawson's integral. Mathematics of Computation, 24, 171-178.
Khan, P.B. (1990) Mathematical Methods for Scientists and Engineers. Linear and Nonlinear Systems. New York: John Wiley & Sons, Inc.
Kurosch, A.G. (1968) Curso de Álgebra Superior. Moscú: Mir.
Lether, F.G. (1997) Constrained near-minimax rational approximations to Dawson's integral. Applied Mathematics and Computation, 88 (2), 267-274.
Lether, F.G. (1998) Shifted rectangular quadrature rule approximations to Dawson's integral F(x). Journal of Computational and Applied Mathematics, 92, 97-102.
McCabe, J.H. (1974) A continued fraction expansion with a truncated error estimate for Dawson’s integral. Math Comput, 28, 811-816
Murley, J. & Saad, N. (2008) Tables of the Appell Hypergeometric Functions F2. arXiv:0809.5203 [math-ph].
Oberguggenberger, M. & Ostermann, A. (2011) Analysis for Computer Scientists: Foundations, Methods, and Algorithms, New York: Springer.
Petrova, A.G., Domingo A. Tarzia, D.A., & Turner, C.V. (1994) The one-phase supercooled Stefan Problem with Temperature Boundary Condition. Advances in mathematical sciences and appliccations. Gakkotosho, Tokyo, 4(1), 35-50.
Prigogine, I. and Rice, S. (2001) Advances in chemical physics, Volume 117. USA: John Wiley and Sons, Inc.
Scott, P. (2007) Comoving coordinate system for relativistic hydrodynamics. Physical Review C, 75(2): 024907. doi:10.1103/PhysRevC.75.024907
Sykora, S. (2012) Dawson’s integral approximations. Published as acode-snnippet in Stan’s library, Ed. S. Sykora. doi:10.3247/SL4soft 12.001. https://goo.gl/9eLDpJ . Accesed August 2017.
Vazquez-Leal, H., & Sarmiento-Reyes, A. (2015) Power Series Extender Method for the Solution of Nonlinear Differential Equations. Mathematical Problems in Engineering, 2015, 1-7. Article ID 717404, doi:10.1155/2015/717404.
Vazquez-Leal, H., Castañeda-Sheissa, R., Filobello-Niño, U., Sarmiento-Reyes, A. & Sanchez-Orea, J. (2012) High Accurate Simple Approximation of Normal Distribution Integral. Mathematical Problems in Engineering. 2012, 1-22. Article ID124029. doi:10.1155/2012/124029.
Weisstein, E.W. (2017) Dawson's integral". From MathWorld-A Wolfram Web Resource. http://mathworld. wolfram./DawsonsIntegral.html. Accessed August 2017.
Zill, D.G. (2012) A First Course in Differential Equations with Modeling Applications, 10TH Edition. Boston: Cengage Learning.