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    <text lang="ger">
      <p bold="true">Gewöhnliche Differenzialgleichungen</p>
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    <text lang="eng">
      <p bold="true">Ordinary Differential Equations</p>
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  <region id="1" left="18" top="45" width="709" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>SMath verfügt über keinerlei eingebaute Funktionen zur Lösung von gewöhnlichen 
Differenzialgleichungen. Allerdings gibt es einige Plugins, die numerische Verfahren
bereitstellen. Zudem bietet das Plugin MapleWrapper Zugriff auf die symbolischen
Lösungsmöglichkeiten mit MapleV.</p>
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    <text lang="eng">
      <p>SMath has no built-in solvers for ordinary differential equations (ODE). However,
there are plugins which provide numerical procedures for the solution of ODEs.
Also, the MapleWrapper Plugin provides access to the symbolic capabilities of MapleV.</p>
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    <text lang="ger">
      <p href="Section Math ODE Intro.sm">Einführung</p>
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    <text lang="eng">
      <p href="Section Math ODE Intro.sm">Introduction</p>
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  <region id="3" left="18" top="144" width="308" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math ODE rate function.sm">Anforderungen an die Ableitungsfunktion D</p>
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    <text lang="eng">
      <p href="Section Math ODE rate function.sm">Requirements for the rate function D</p>
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  <region id="4" left="18" top="162" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math ODE precision.sm">Genauigkeitssteuerung</p>
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    <text lang="eng">
      <p href="Section Math ODE precision.sm">Precision control</p>
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  <region id="5" left="18" top="180" width="258" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math ODE examples uni.sm">Beispiele für DGL 2. Ordnung</p>
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    <text lang="eng">
      <p href="Section Math ODE examples uni.sm">Examples for second order ODEs</p>
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    <text lang="ger">
      <p href="Section Math ODE examples multiline uni.sm">Beispiel für eine Ableitungsfunktion mit Anweisungsblock</p>
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    <text lang="eng">
      <p href="Section Math ODE examples multiline uni.sm">Example for a multi-line rate function</p>
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  <region id="7" left="18" top="252" width="175" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Solver in the plugin</p>
    </text>
  </region>
  <region id="8" left="198" top="252" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Alglib.sm">Alglib</p>
    </text>
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  <region id="9" left="18" top="288" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="al_rkckadapt.sm">al_rkckadapt()</p>
    </text>
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  <region id="10" left="243" top="288" width="374" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Runge-Kutta-Cash-Karp Löser für Systeme nichtlinearer DGL</p>
    </text>
    <text lang="eng">
      <p>Runge-Kutta-Cash-Karp solver for ODE systems</p>
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  <region id="11" left="18" top="324" width="175" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Solver in the plugin</p>
    </text>
  </region>
  <region id="12" left="198" top="324" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin DotNumerics.sm">DotNumerics</p>
    </text>
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  <region id="13" left="18" top="360" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="dn_AdamsMoulton.sm">dn_AdamsMoulton()</p>
    </text>
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  <region id="14" left="243" top="360" width="364" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Adams-Moulton Verfahren für steife GDG-Systeme</p>
    </text>
    <text lang="eng">
      <p>stiff ODE solver using Adams-Moulton method</p>
    </text>
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  <region id="15" left="18" top="378" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="dn_ExplicitRK45.sm">dn_ExplicitRK45()</p>
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  <region id="16" left="243" top="378" width="448" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Êxplizites Runge-Kutta-Verfahren für nichtsteife GDG-Systeme</p>
    </text>
    <text lang="eng">
      <p>Explicit Runge-Kutta method for non-stiff ODE systems</p>
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  <region id="17" left="18" top="396" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="dn_GearsBDF.sm">dn_GearsBDF()</p>
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  <region id="18" left="243" top="396" width="372" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gears BDF-Verfahren für nichtsteife GDG Systeme</p>
    </text>
    <text lang="eng">
      <p>non-stiff ODE solver using Gear's BDF method</p>
    </text>
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  <region id="19" left="18" top="414" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="dn_ImplicitRK5.sm">dn_ImplicitRK5()</p>
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  <region id="20" left="243" top="414" width="422" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Implizites Runge-Kutta-Verfahren für steife GDG-Systme</p>
    </text>
    <text lang="eng">
      <p>stiff ODE solver using implicit Runge-Kutta method</p>
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    <text lang="ger">
      <p bold="true">Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Solver in the plugin</p>
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  <region id="22" left="198" top="450" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin ODE Solver.sm">ODE Solver</p>
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  </region>
  <region id="23" left="18" top="486" width="250" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Mathcad-kompatible Funktionen</p>
    </text>
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  <region id="24" left="18" top="513" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Rkadapt.sm">Rkadapt()</p>
    </text>
  </region>
  <region id="25" left="243" top="513" width="406" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Runge-Kutta-Verfahren mit adaptiver Schrittweite</p>
    </text>
    <text lang="eng">
      <p>ODE solver (Runge-Kutta with adaptive step size)</p>
    </text>
  </region>
  <region id="26" left="18" top="531" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="rkfixed.sm">rkfixed()</p>
    </text>
  </region>
  <region id="27" left="243" top="531" width="381" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Runge-Kutta-Verfahren mit fester Schrittweite</p>
    </text>
    <text lang="eng">
      <p>ODE solver (Runge-Kutta with fixed step size)</p>
    </text>
  </region>
  <region id="28" left="18" top="558" width="340" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Löser aus der Intel ODE Solver Library</p>
    </text>
    <text lang="eng">
      <p underline="true">Solver from the Intel ODE Solver Library</p>
    </text>
  </region>
  <region id="29" left="18" top="585" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="mk52lfa.sm">mk52lfa()</p>
    </text>
  </region>
  <region id="30" left="243" top="585" width="380" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Impliziter Löser mit analytischer Jacobi-Matrix </p>
    </text>
    <text lang="eng">
      <p>Implicit solver with analytical Jacobi matrix</p>
    </text>
  </region>
  <region id="31" left="18" top="603" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="mk52lfn.sm">mk52lfn()</p>
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  <region id="32" left="243" top="603" width="372" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Impliziter Löser mit numerischer Jacobi-Matrix </p>
    </text>
    <text lang="eng">
      <p>Implicit solver with numerical Jacobi matrix</p>
    </text>
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  <region id="33" left="18" top="621" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="rkm9mka.sm">rkm9mka()</p>
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  <region id="34" left="243" top="621" width="434" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Löser für Systeme variabler oder unbekannter Steifigkeit</p>
    </text>
    <text lang="eng">
      <p>Solver for systems of variable or unknown stiffness </p>
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  <region id="35" left="18" top="639" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="rkm9mkn.sm">rkm9mkn()</p>
    </text>
  </region>
  <region id="36" left="243" top="639" width="434" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Löser für Systeme variabler oder unbekannter Steifigkeit</p>
    </text>
    <text lang="eng">
      <p>Solver for systems of variable or unknown stiffness </p>
    </text>
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  <region id="37" left="18" top="657" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="rkm9mst.sm">rkm9st()</p>
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  <region id="38" left="243" top="657" width="336" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Löser für nicht- oder moderat steife Systeme</p>
    </text>
    <text lang="eng">
      <p>Solver for non- or middle-stiff systems </p>
    </text>
  </region>
  <region id="39" left="18" top="702" width="175" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Solver in the plugin</p>
    </text>
  </region>
  <region id="40" left="198" top="702" width="168" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Matlab lib.sm">Matlab C++ Math lib</p>
    </text>
  </region>
  <region id="41" left="18" top="738" width="94" height="24" color="#000000" bgColor="#c0c0c0" fontSize="10">
    <text lang="ger">
      <p href="mwode113.sm">mwode113()</p>
    </text>
  </region>
  <region id="42" left="243" top="738" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ODE solver</p>
    </text>
  </region>
  <region id="43" left="18" top="756" width="94" height="24" color="#000000" bgColor="#c0c0c0" fontSize="10">
    <text lang="ger">
      <p href="mwode15s.sm">mwode15s()</p>
    </text>
  </region>
  <region id="44" left="243" top="756" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ODE solver</p>
    </text>
  </region>
  <region id="45" left="18" top="774" width="86" height="24" color="#000000" bgColor="#c0c0c0" fontSize="10">
    <text lang="ger">
      <p href="mwode23.sm">mwode23()</p>
    </text>
  </region>
  <region id="46" left="243" top="774" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ODE solver</p>
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  </region>
  <region id="47" left="18" top="792" width="94" height="24" color="#000000" bgColor="#c0c0c0" fontSize="10">
    <text lang="ger">
      <p href="mwode23s.sm">mwode23s()</p>
    </text>
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  <region id="48" left="243" top="792" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ODE solver</p>
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  <region id="49" left="18" top="810" width="86" height="24" color="#000000" bgColor="#c0c0c0" fontSize="10">
    <text lang="ger">
      <p href="mwode45.sm">mwode45()</p>
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  <region id="50" left="243" top="810" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ODE solver</p>
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  <region id="51" left="18" top="846" width="175" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Solver in the plugin</p>
    </text>
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  <region id="52" left="198" top="846" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin GNU Scientific Library.sm">GNU Scientific Library</p>
    </text>
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  <region id="53" left="18" top="882" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="gslrk2.sm">gslrk2()</p>
    </text>
  </region>
  <region id="54" left="243" top="882" width="374" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Explicit embedded Runge-Kutta (2, 3) method.</p>
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  <region id="55" left="18" top="900" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
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      <p href="gslrk4.sm">gslrk4()</p>
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  <region id="56" left="243" top="900" width="366" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Explicit 4th order (classical) Runge-Kutta.</p>
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  <region id="57" left="18" top="918" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="gslrk8pd.sm">gslrk8pd()</p>
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  <region id="58" left="243" top="918" width="497" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.</p>
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  <region id="59" left="18" top="936" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="gslrkck.sm">gslrkck()</p>
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  </region>
  <region id="60" left="243" top="936" width="456" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.</p>
    </text>
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  <region id="61" left="18" top="954" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="gslrkf45.sm">gslrkf45()</p>
    </text>
  </region>
  <region id="62" left="243" top="954" width="448" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Explicit embedded Runge-Kutta-Fehlberg (4, 5) method.</p>
    </text>
  </region>
  <region id="63" left="18" top="990" width="241" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Symbolischer Löser im Plugin</p>
    </text>
    <text lang="eng">
      <p bold="true">Symbolic Solver in the plugin</p>
    </text>
  </region>
  <region id="64" left="297" top="990" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Maxima.sm">Maxima</p>
    </text>
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  <region id="65" left="18" top="1026" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="ODE.2.sm">ODE.2()</p>
    </text>
  </region>
  <region id="66" left="243" top="1026" width="307" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>DGL-Löser, basierend auf Maximas ode2() </p>
    </text>
    <text lang="eng">
      <p>ODE solver, based on Maxima's ode2()</p>
    </text>
  </region>
  <region id="67" left="18" top="1089" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
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  <region id="68" left="18" top="1107" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
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    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
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  <region id="69" left="18" top="1143" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-11-10 18:06:03 +0100 (So, 10. Nov 2013) $ </p>
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