<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332016000200389</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una introducción al método libre de malla de Conjuntos Finitos De Puntos]]></article-title>
<article-title xml:lang="en"><![CDATA[An introduction to the meshless Finite Pointset Method]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[RuizV.]]></surname>
<given-names><![CDATA[JorgeMauricio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[LeónE.]]></surname>
<given-names><![CDATA[DiegoA.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[ Bogotá]]></addr-line>
<country>CO</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[ Bogotá]]></addr-line>
<country>CO</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<volume>23</volume>
<numero>2</numero>
<fpage>389</fpage>
<lpage>408</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332016000200389&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332016000200389&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332016000200389&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEste trabajo propone una introducción corta y simple al método libre de malla conocido con el nombre de método de conjuntos finitos de puntos (FPM). Se describen los conceptos importantes que involucra el método como: la generación del sistema de puntos, búsqueda de puntos vecinos, aproximación de las derivadas espaciales mediante el método de mínimos cuadrados móviles y la solución de sistemas de ecuaciones diferenciales ordinarias resultantes. Como aplicación del método FPM se soluciona la ecuación viscosa y no viscosa de Burgers. Las soluciones numéricas son comparadas con la solución analítica y se realiza un análisis de convergencia del método vía experimentación numérica. Se proveen las rutinas de MATLAB de los pasos fundamentales del método FPM, que pueden ser usados para resolver problemas más complicados.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractIn this work we propose a short and simple introduction of the meshless method known as finite pointset method (FPM).We describe the main concepts involved in the FPM method like: the pointset generation, point neighbors search, the spatial derivatives approximation by the moving least square method and the solution of the resultant ordinary differential system. As application of the method we solve the viscid an inviscid Bugers equation. The numerical solutions are compared with the analytical solution and a convergence analysis via numerical experimentation is performed. We provide the MATLAB codes for the main steps of the FPM method, which can be used to solve more complex problems.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[métodos sin malla]]></kwd>
<kwd lng="es"><![CDATA[mínimos cuadrados móviles]]></kwd>
<kwd lng="es"><![CDATA[ecuación de Burgers]]></kwd>
<kwd lng="en"><![CDATA[meshless method]]></kwd>
<kwd lng="en"><![CDATA[moving least square method]]></kwd>
<kwd lng="en"><![CDATA[Burgers equation]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Error estimates for moving least square approximations]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Armentano]]></surname>
<given-names><![CDATA[M.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Durán]]></surname>
<given-names><![CDATA[R.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied Numerical Mathematics]]></source>
<year>2001</year>
<volume>37</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>397-416</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Moving least squares particle hydrodynamics I, consistency and stability]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dilts]]></surname>
<given-names><![CDATA[G.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Int. J. Numer. Meth. Engng]]></source>
<year>1999</year>
<volume>44</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1115-55</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Finite difference techniques for variable grids]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jensen]]></surname>
<given-names><![CDATA[P.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computers &amp; Structures]]></source>
<year>1972</year>
<volume>2</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>17-29</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kröner]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Schemes for Conservation Laws]]></source>
<year>1997</year>
<publisher-loc><![CDATA[New-York ]]></publisher-loc>
<publisher-name><![CDATA[Wiley Teubner]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kuhnert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[General Smoothed Particle Hydrodynamics]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Kaiserslautern, Germany ]]></publisher-loc>
<publisher-name><![CDATA[Kaiserslautern University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Surfaces generated by moving least square methods]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lancaster]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Salkauskas]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Math of Comp]]></source>
<year>1981</year>
<volume>37</volume>
<numero>155</numero>
<issue>155</issue>
<page-range>141-58</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[On generalized moving least squares and diffuse derivatives]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mirzaei]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Schaback]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Dehghan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[IMA J Numer Anal]]></source>
<year>2012</year>
<volume>32</volume>
<page-range>983-1000</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Moeller]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Influence of the counter blow air flow during container glass blow and blow process]]></source>
<year>2014</year>
<conf-name><![CDATA[ Proceedings 12th ESG (European Glass Society)]]></conf-name>
<conf-date>21-24 September 2014</conf-date>
<conf-loc>Parma, Italy </conf-loc>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Morris]]></surname>
<given-names><![CDATA[J.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[An overview of the method of smoothed particle hydrodynamics]]></source>
<year>1995</year>
<publisher-loc><![CDATA[Germany ]]></publisher-loc>
<publisher-name><![CDATA[Technische Universität Kaiserslautern]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[A finite point method in computational mechanics. Applications to convective transport and fluid flow]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Oñate]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Idelsohn]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Zienkiewicz]]></surname>
<given-names><![CDATA[O.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Taylor]]></surname>
<given-names><![CDATA[R.L.]]></given-names>
</name>
</person-group>
<source><![CDATA[International Journal for Numerical Methods in Engineering]]></source>
<year>1996</year>
<volume>39</volume>
<numero>22</numero>
<issue>22</issue>
<page-range>3839-66</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Paiva]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Petronetto]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Tavares]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Lewiner]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Simulacão de Fluidos sem Malha: Uma introducão ao método SPH]]></source>
<year>2009</year>
<conf-name><![CDATA[ 27Colóquio Brasileiro de Matemática]]></conf-name>
<conf-loc>Rio de Janeiro </conf-loc>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Prätzel-Wolters]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Jahresberichte Fraunhofer Institut für Technound Wirtschaftsmathematik ITWM]]></source>
<year>2014</year>
<publisher-loc><![CDATA[Kaiserslautern ]]></publisher-loc>
<publisher-name><![CDATA[Kerner Druck GmbH]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Modelling incompressible NavierStokes Flows by LSQ-SPH]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tiwari]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Manservisi]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Nepali Math Sc. Report]]></source>
<year>2002</year>
<volume>20</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>1-23</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
