예제: 단위를 포함하여 pdesolve 사용

함수 > 풀이 및 최적화 > 풀이 구간 함수 > 예제: 단위를 포함하여 pdesolve 사용

열전도 방정식을 풀려면 pdesolve 함수를 사용합니다.

1. 다음 입력 매개 변수를 생성합니다. nTime 및 nX는 격자선 점의 수입니다.τMax는 trange의 상한값이고 a는 계수입니다.

2. PDE 풀이 블록을 설정합니다. 열전도 방정식을 사용하고 초기 조건 세트를 추가합니다. 풀이 구간 내부에서는 단위(m)를 사용합니다.

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  <solveblock>
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                    <id xml:space="preserve">x</id>
                    <id xml:space="preserve">t</id>
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            <real>0</real>
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              </id>
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                <apply>
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                  <real>0</real>
                  <id xml:space="preserve">m</id>
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                <id xml:space="preserve">t</id>
              </sequence>
            </apply>
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                    <real>10</real>
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                        <real>-0.1</real>
                        <id xml:space="preserve">t</id>
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                </parens>
              </apply>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
              </apply>
            </apply>
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            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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        </math>
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              </id>
              <sequence>
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                  <scale />
                  <real>1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
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                <id xml:space="preserve">t</id>
              </sequence>
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            <apply>
              <scale />
              <real>0</real>
              <apply>
                <div />
                <real>1</real>
                <id labels="UNIT" xml:space="preserve">m</id>
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              <id xml:space="preserve">T</id>
              <sequence>
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                <real>0</real>
              </sequence>
            </apply>
            <real>0</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
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        <math resultRef="36">
          <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>
                  </apply>
                  <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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              </sequence>
            </apply>
          </define>
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            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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3. 3D 도표에 해를 시각화하려면 CreateMesh 함수를 사용합니다.

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            <real>1</real>
            <id labels="UNIT" xml:space="preserve" label-is-contextual="true">m</id>
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          <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>
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    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
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4. 3D 도표를 사용하여 해를 도표화합니다.

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            <startValue />
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        </yAxis>
        <zAxis start="-0.00055" end="0.00165" rank="1">
          <axisLine />
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            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
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            <tickMarks display="true" />
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          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue />
            <endValue />
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        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">U</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.0011441619532079339</Cell>
          <Cell>0.091956017087953423</Cell>
          <Cell>0.9957624123327542</Cell>
          <Cell>0</Cell>
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          <Cell>0</Cell>
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          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
          <Cell>0</Cell>
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        </Cells>
      </CameraTransformMatrix>
      <CameraType>Orthographic</CameraType>
    </plot3D>
  </plot>
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5. 등고선도를 사용하여 해를 도표화합니다.