Esempio: utilizzo di pdesolve con le unità

Funzioni > Soluzione e ottimizzazione > Funzioni del blocco di soluzione > Esempio: utilizzo di pdesolve con le unità

È possibile utilizzare la funzione pdesolve per risolvere l'equazione del calore.

1. Creare i seguenti parametri di input: nTime e nX indicano il numero di punti della griglia.τMax è il limite superiore di trange e a è un coefficiente.

2. Impostare il blocco di soluzione di equazioni differenziali alle derivate parziali. Utilizzare l'equazione del calore e aggiungere un insieme di condizioni iniziali. Utilizzare le unità (m) all'interno del blocco di soluzione.

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              </id>
              <sequence>
                <apply>
                  <scale />
                  <real>0</real>
                  <id xml:space="preserve">m</id>
                </apply>
                <id xml:space="preserve">t</id>
              </sequence>
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                    <scale />
                    <real>10</real>
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                      <id xml:space="preserve">e</id>
                      <apply>
                        <scale />
                        <real>-0.1</real>
                        <id xml:space="preserve">t</id>
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                    </apply>
                  </apply>
                </parens>
              </apply>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
              </apply>
            </apply>
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                  <real>1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
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                <id xml:space="preserve">t</id>
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            <apply>
              <scale />
              <real>0</real>
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                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
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                <real>0</real>
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            <real>0</real>
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          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">T</id>
            <apply>
              <id labels="KEYWORD" xml:space="preserve">Pdesolve</id>
              <sequence>
                <id labels="VARIABLE" xml:space="preserve">T</id>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">x</id>
                <matrix rows="2" cols="1">
                  <apply>
                    <scale />
                    <real>0</real>
                    <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
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                  <apply>
                    <scale />
                    <real>1</real>
                    <id labels="UNIT" xml:space="preserve">m</id>
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                </matrix>
                <id xml:space="preserve">t</id>
                <matrix rows="2" cols="1">
                  <real>0</real>
                  <id labels="VARIABLE" xml:space="preserve">τMax</id>
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3. Per visualizzare la soluzione in un grafico 3D, utilizzare la funzione CreateMesh.

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            <real>0</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <apply>
            <scale />
            <real>1</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
          </apply>
          <real>0</real>
          <id labels="VARIABLE" xml:space="preserve">τMax</id>
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">nX</id>
          <id labels="VARIABLE" xml:space="preserve">nTime</id>
        </sequence>
      </apply>
    </define>
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4. Tracciare la soluzione utilizzando un grafico 3D.

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        <zAxis start="-0.00055" end="0.00165" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <numberFormat>
            <general precision="3" />
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          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
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          <math>
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        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.0011441619532079339</Cell>
          <Cell>0.091956017087953423</Cell>
          <Cell>0.9957624123327542</Cell>
          <Cell>0</Cell>
          <Cell>0.32809858802063024</Cell>
          <Cell>0.94060649816846953</Cell>
          <Cell>-0.087239510212507962</Cell>
          <Cell>0</Cell>
          <Cell>-0.94464279356394487</Cell>
          <Cell>0.32680805761879472</Cell>
          <Cell>-0.029094433198413844</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0.8341587442339774</Cell>
        </Cells>
      </CameraTransformMatrix>
      <CameraType>Orthographic</CameraType>
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5. Tracciare la soluzione utilizzando un grafico a curve di livello.

Argomenti correlati

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Esempio: aggiunta di unità a blocchi di soluzione

CreateSpace e CreateMesh

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