Numerical resolution of Emden's equation using Adomian polynomials
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Título: | Numerical resolution of Emden's equation using Adomian polynomials |
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Autor/es: | Pujol López, María José | Pujol, Francisco A. | Aznar Gregori, Fidel | Pujol, Mar | Rizo, Ramón |
Grupo/s de investigación o GITE: | Informática Industrial e Inteligencia Artificial |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Ciencia de la Computación e Inteligencia Artificial |
Palabras clave: | Emden's equation | Power series | Frobenius method | Adomian polynomials | Decomposition method | Polynomials | Fluids | Flow |
Área/s de conocimiento: | Ciencia de la Computación e Inteligencia Artificial |
Fecha de publicación: | 2013 |
Editor: | Emerald Group Publishing Limited |
Cita bibliográfica: | International Journal of Numerical Methods for Heat & Fluid Flow. 2013, 23(6): 1012-1022. doi:10.1108/HFF-05-2011-0109 |
Resumen: | Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods. |
Patrocinador/es: | This work has been supported by the Ministerio de Ciencia e Innovación, project TIN2009-10581. |
URI: | http://hdl.handle.net/10045/41660 |
ISSN: | 0961-5539 (Print) | 1758-6585 (Online) |
DOI: | 10.1108/HFF-05-2011-0109 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © Emerald Group Publishing Limited |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1108/HFF-05-2011-0109 |
Aparece en las colecciones: | INV - i3a - Artículos de Revistas |
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Archivo | Descripción | Tamaño | Formato | |
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2013_Pujol_etal_Emden-equation.pdf | Versión revisada (acceso abierto) | 75,74 kB | Adobe PDF | Abrir Vista previa |
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