<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012016000100083</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[New galerkin operational matrices for solving lane-Emden type equations]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Abd-Elhameed]]></surname>
<given-names><![CDATA[W.M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="A a"/>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Doha]]></surname>
<given-names><![CDATA[E.H.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[A.S.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bassuony]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,University of Jeddah Faculty of Science Department of Mathematics]]></institution>
<addr-line><![CDATA[Jeddah ]]></addr-line>
<country>Saudi Arabia</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Cairo University Faculty of Science Department of Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Egypt</country>
</aff>
<aff id="A03">
<institution><![CDATA[,National Research Institute of Astronomy and Geophysics Department of Astronomy ]]></institution>
<addr-line><![CDATA[Cairo ]]></addr-line>
<country>Egypt</country>
</aff>
<aff id="A04">
<institution><![CDATA[,Fayoum University Faculty of Science Department of Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Egypt</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2016</year>
</pub-date>
<volume>52</volume>
<numero>1</numero>
<fpage>83</fpage>
<lpage>92</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012016000100083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012016000100083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012016000100083&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n = 3 to show that the suggested solutions in this paper are in good agreement with the numerical results.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Las ecuaciones tipo Lane-Emden se usan para modelar fenómenos en la física matemática y en la astrofísica, tales como explosiones térmicas. Presentamos matrices operacionales de Chebyshev-Galerkin de tercera y cuarta clase para la solución de este tipo de problemas. La idea principal se basa en la conversión, mediante métodos espectrales, de la ecuación lineal o no lineal de Lane-Emden en un sistema de ecuaciones lineales o no lineales de los coeficientes de expansión, el cual se resuelve eficientemente. La principal ventaja del algoritmo propuesto en el caso lineal es que los sistemas lineales resultantes están estructurados, lo cual facilita el cómputo. Como aplicación, consideramos un modelo politrópico con n = 3 para el Sol y mostramos que las soluciones que proponemos concuerdan con los resultados numéricos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[methods: analytical]]></kwd>
<kwd lng="en"><![CDATA[methods: numerical]]></kwd>
<kwd lng="en"><![CDATA[stars: solar-type]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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