<?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>0187-6236</journal-id>
<journal-title><![CDATA[Atmósfera]]></journal-title>
<abbrev-journal-title><![CDATA[Atmósfera]]></abbrev-journal-title>
<issn>0187-6236</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Ciencias de la Atmósfera y Cambio Climático]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0187-62362023000300120</article-id>
<article-id pub-id-type="doi">10.20937/atm.53172</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Solution of advection-diffusion-reaction problems on a sphere: High-resolution numerical experiments]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[Yuri N.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cruz-Rodriguez]]></surname>
<given-names><![CDATA[Roberto C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[Denis M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Ciencias de la Atmósfera y Cambio Climático ]]></institution>
<addr-line><![CDATA[Mexico City ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Sceptica Scientific  ]]></institution>
<addr-line><![CDATA[Bramhall ]]></addr-line>
<country>UK</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<volume>37</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0187-62362023000300120&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0187-62362023000300120&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0187-62362023000300120&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT The implicit and unconditionally stable numerical method proposed in Skiba (2015) is applied to solve linear advection-diffusion-reaction problems and nonlinear diffusion-reaction problems on a sphere. Numerical experiments carried out on a high-resolution spherical mesh show the effectiveness of the method in modelling linear advection-diffusion processes on a sphere (dispersion of pollution in the atmosphere), and nonlinear diffusion processes (propagation of nonlinear temperature waves, blow-up regimes of combustion, and chemical reactions in the Gray-Scott model). The method correctly describes the mass balance of a substance in forced and dissipative systems and conserves the total mass and norm of the solution in the absence of forcing and dissipation.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN El método numérico implícito e incondicionalmente estable propuesto por Skiba (2015) se aplica para resolver problemas lineales de advección-difusión-reacción y no lineales de difusión-reacción sobre una esfera. Los experimentos numéricos realizados sobre una malla esférica de alta resolución muestran la eficacia del método para modelar procesos de advección-difusión lineales sobre una esfera (dispersión de la contaminación en la atmósfera), y procesos de difusión no lineal (propagación de ondas de temperatura no lineales, regímenes blow-up de combustión y reacciones químicas en el modelo de Gray-Scott). El método describe correctamente el balance de masa de una sustancia en sistemas forzados y disipativos, y conserva la masa total y la norma de la solución en ausencia de forzamiento y disipación.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Advection-diffusion problems]]></kwd>
<kwd lng="en"><![CDATA[temperature waves of nonlinear combustion]]></kwd>
<kwd lng="en"><![CDATA[blow-up regimes of nonlinear combustion]]></kwd>
<kwd lng="en"><![CDATA[Gray-Scott nonlinear chemical model]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bekman]]></surname>
<given-names><![CDATA[I.N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical theory of diffusion]]></source>
<year>1990</year>
<publisher-name><![CDATA[Moscow University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cruz-Rodríguez]]></surname>
<given-names><![CDATA[RC]]></given-names>
</name>
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[DM]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An implicit direct unconditionally stable numerical algorithm for the solution of advection-diffusion equation on a sphere]]></article-title>
<source><![CDATA[Applied Numerical Mathematics]]></source>
<year>2019</year>
<volume>142</volume>
<page-range>1-15</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giraldo]]></surname>
<given-names><![CDATA[FX]]></given-names>
</name>
<name>
<surname><![CDATA[Rosmond]]></surname>
<given-names><![CDATA[TE]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A scalable spectral element Eulerian atmospheric model (SEE-AM) for NWP: Dynamical core tests]]></article-title>
<source><![CDATA[Monthly Weather Review]]></source>
<year>2004</year>
<volume>132</volume>
<page-range>133-53</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Glicksman]]></surname>
<given-names><![CDATA[ME]]></given-names>
</name>
</person-group>
<source><![CDATA[Diffusion in solids: field theory, solid-state principles and applications]]></source>
<year>2000</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gray]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Scott]]></surname>
<given-names><![CDATA[SK]]></given-names>
</name>
</person-group>
<source><![CDATA[Chemical oscillations and instabilities: non-linear chemical kinetics]]></source>
<year>1994</year>
<publisher-loc><![CDATA[Oxford ]]></publisher-loc>
<publisher-name><![CDATA[Clarendon Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Har-Shemesh]]></surname>
<given-names><![CDATA[O]]></given-names>
</name>
<name>
<surname><![CDATA[Quax]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
<name>
<surname><![CDATA[Hoekstra]]></surname>
<given-names><![CDATA[AG]]></given-names>
</name>
<name>
<surname><![CDATA[Sloot]]></surname>
<given-names><![CDATA[PMA]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction-diffusion model]]></article-title>
<source><![CDATA[Journal of Statistical Mechanics: Theory and Experiment]]></source>
<year>2016</year>
<page-range>1-20</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kurdyumov]]></surname>
<given-names><![CDATA[SP]]></given-names>
</name>
</person-group>
<source><![CDATA[Regimes with blow-up]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Moscow ]]></publisher-loc>
<publisher-name><![CDATA[Fizmatlit]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lax]]></surname>
<given-names><![CDATA[PD]]></given-names>
</name>
<name>
<surname><![CDATA[Richtmyer]]></surname>
<given-names><![CDATA[RD]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Survey of the stability of linear finite difference equations]]></article-title>
<source><![CDATA[Communications on Pure and Applied Mathematics]]></source>
<year>1956</year>
<volume>9</volume>
<page-range>267-93</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Majewski]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
<name>
<surname><![CDATA[Liermann]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Prohl]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Ritter]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
<name>
<surname><![CDATA[Buchhold]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Hanisch]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
<name>
<surname><![CDATA[Paul]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
<name>
<surname><![CDATA[Wergen]]></surname>
<given-names><![CDATA[W]]></given-names>
</name>
<name>
<surname><![CDATA[Baumgardner]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The operational global icosahedral-hexagonal gridpoint model GME: description and high-resolution tests]]></article-title>
<source><![CDATA[Monthly Weather Review]]></source>
<year>2002</year>
<volume>130</volume>
<page-range>319-38</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Marchuk]]></surname>
<given-names><![CDATA[GI]]></given-names>
</name>
</person-group>
<source><![CDATA[Methods of Numerical Mathematics]]></source>
<year>1982</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pearson]]></surname>
<given-names><![CDATA[JE]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Complex patterns in a simple system]]></article-title>
<source><![CDATA[Science]]></source>
<year>1993</year>
<volume>261</volume>
<page-range>189-92</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pudykiewicz]]></surname>
<given-names><![CDATA[JA]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Numerical solution of the reaction-advection-diffusion equation on the sphere]]></article-title>
<source><![CDATA[Journal of Computational Physics]]></source>
<year>2006</year>
<volume>213</volume>
<page-range>358-90</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sherman]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Morrison]]></surname>
<given-names><![CDATA[WJ]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Adjustment of an inverse matrix corresponding to a change in one element of a given matrix]]></article-title>
<source><![CDATA[Annals of Mathematical Statistics]]></source>
<year>1950</year>
<volume>21</volume>
<page-range>124-7</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A non-iterative implicit algorithm for the solution of advection-diffusion equation on a sphere]]></article-title>
<source><![CDATA[International Journal for Numerical Methods in Fluids]]></source>
<year>2015</year>
<volume>78</volume>
<page-range>257-82</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical problems of the dynamics of incompressible fluid on a rotating sphere]]></source>
<year>2017</year>
<publisher-loc><![CDATA[Cham, Switzerland ]]></publisher-loc>
<publisher-name><![CDATA[Springer Intern. Publ. AG.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
<name>
<surname><![CDATA[Cruz-Rodriguez]]></surname>
<given-names><![CDATA[RC]]></given-names>
</name>
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[DM]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solution of linear and nonlinear advection-diffusion problems on a sphere]]></article-title>
<source><![CDATA[Numerical Methods for Partial Differential Equations]]></source>
<year>2020</year>
<volume>36</volume>
<page-range>1922-37</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[DM]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On an efficient splitting-based method for solving the diffusion equation on a sphere]]></article-title>
<source><![CDATA[Numerical Methods for Partial Differential Equations]]></source>
<year>2012</year>
<volume>28</volume>
<page-range>331-52</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[DM]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Splitting-based schemes for numerical solution of a nonlinear diffusion equation on a sphere]]></article-title>
<source><![CDATA[Applied Mathematics and Computation]]></source>
<year>2013</year>
<volume>219</volume>
<page-range>8467-85</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skiba]]></surname>
<given-names><![CDATA[YN]]></given-names>
</name>
<name>
<surname><![CDATA[Filatov]]></surname>
<given-names><![CDATA[DM]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modelling of combustion and diverse blow-up regimes in a spherical shell. In]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Quintela]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Barral]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
<name>
<surname><![CDATA[Peña]]></surname>
<given-names><![CDATA[FJ]]></given-names>
</name>
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Salgado]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Vázquez-Méndezet]]></surname>
<given-names><![CDATA[ME]]></given-names>
</name>
</person-group>
<source><![CDATA[Progress in Industrial Mathematics at ECMI 2016]]></source>
<year>2017</year>
<page-range>729-35</page-range><publisher-loc><![CDATA[Heidelberg ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Staniforth]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Thuburn]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Horizontal grids for global weather and climate prediction models: a review]]></article-title>
<source><![CDATA[Quarterly Journal of the Royal Meteorological Society]]></source>
<year>2012</year>
<volume>138</volume>
<page-range>1-26</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thomas]]></surname>
<given-names><![CDATA[LH]]></given-names>
</name>
</person-group>
<source><![CDATA[Elliptic problems in linear differential equations over a network. Watson Scientific Computing Laboratory Report]]></source>
<year>1949</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Columbia University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nishiura]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
<name>
<surname><![CDATA[Ueyama]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Spatio-temporal chaos for the Gray-Scott model]]></article-title>
<source><![CDATA[Physica D]]></source>
<year>2001</year>
<volume>150</volume>
<page-range>137-62</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vorob&#8217;yov]]></surname>
<given-names><![CDATA[AKh]]></given-names>
</name>
</person-group>
<source><![CDATA[Diffusion problems in chemical kinetics]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Moscow ]]></publisher-loc>
<publisher-name><![CDATA[Moscow University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Williamson]]></surname>
<given-names><![CDATA[DL]]></given-names>
</name>
<name>
<surname><![CDATA[Drake]]></surname>
<given-names><![CDATA[JB]]></given-names>
</name>
<name>
<surname><![CDATA[Hack]]></surname>
<given-names><![CDATA[JJ]]></given-names>
</name>
<name>
<surname><![CDATA[Jacob]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
<name>
<surname><![CDATA[Swarztrauber]]></surname>
<given-names><![CDATA[PN]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A standard test set for numerical approximations to the shallow water equations in spherical geometry]]></article-title>
<source><![CDATA[Journal of Computational Physics]]></source>
<year>1992</year>
<volume>102</volume>
<page-range>211-24</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
