RosettaCodeData/Task/Runge-Kutta-method/Phix/runge-kutta-method.phix

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 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #008080;">constant</span> <span style="color: #000000;">dt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.1</span>
 <span style="color: #004080;">atom</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1.0</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"  x    true/actual y   calculated y    relative error\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ---   -------------   -------------   --------------\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
     <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dt</span>
     <span style="color: #008080;">if</span> <span style="color: #004080;">integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
         <span style="color: #004080;">atom</span> <span style="color: #000000;">act</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">16</span>
         <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%4.1f  %14.9f  %14.9f   %.9e\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">act</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">-</span><span style="color: #000000;">act</span><span style="color: #0000FF;">)})</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #004080;">atom</span> <span style="color: #000000;">k1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">),</span>
          <span style="color: #000000;">k2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k1</span><span style="color: #0000FF;">),</span>
          <span style="color: #000000;">k3</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k2</span><span style="color: #0000FF;">),</span>
          <span style="color: #000000;">k4</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k3</span><span style="color: #0000FF;">)</span>
     <span style="color: #000000;">y</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dt</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">k1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">k2</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k3</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">k4</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">6</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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