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Euler method (view source)

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=={{header|Phix}}==
{{Translibheader|CPhix/pGUI}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/euler_method.htm here].
<!--<lang Phix>(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\Euler_method.exw
-- =============================
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constantfunction</span> <span style="color: #000000;">FMTivp_euler</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #008000000000;">f</span><span style="color: %7.3f#0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">end_t</span><span style="color: #0000FF;">)</span>
<span style="color: #008080004080;">whilesequence</span> <span style="color: #000000;">tres</span> <span style="color: #0000FF;"><=</span><span style="color: #000000;">end_t</span> <span style="color: #0080800000FF;">do{}</span>▼
<span style="color: #008080;">procedure</span> <span style="color: #000000;">ivp_euler</span><span style="color: #0000FF008080;">(</span><span style="color: #004080;">atomfor</span> <span style="color: #000000;">yt</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">f0</span> <span style="color: #0000FF008080;">,to</span> <span style="color: #000000;">stepend_t</span> <span style="color: #0000FF008080;">,by</span> <span style="color: #000000;">end_tstep</span> <span style="color: #0000FF008080;">)do</span>
<span style="color: #004080008080;">integerif</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">y</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">" Step %2d: "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>▼
▲ <span style="color: #008080;">while</span> <span style="color: #000000;">t</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">end_t</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</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: #000000;">FMT</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>▼
<span style="color: #000000;">y</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">step</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">call_func</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">t</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">step</span>▼
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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;">end</span> <span style="color: #008080;">procedure</span>▼
<span style="color: #008080;">procedure</span> <span style="color: #000000;">analytic</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;">" Time: "</span><span style="color: #0000FF;">)</span>▼
<span style="color: #008080;">for</span> <span style="color: #000000;">t</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;">by</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</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;">" %7g"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"\nAnalytic: "</span><span style="color: #0000FF;">)</span>▼
<span style="color: #008080;">for</span> <span style="color: #000000;">t</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;">by</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</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: #000000;">FMT</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">80</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">0.07</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">))</span>▼
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8008080;">printfreturn</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;">);res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedurefunction</span>
▲ <span style="color: #008080;">procedurefunction</span> <span style="color: #000000;">analytic</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
▲ <span style="color: #008080;">for</span> <span style="color: #000000;">t</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;">by</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">20</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">80</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">0.07</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
▲ <span style="color: #008080;">end</span> <span style="color: #008080;">whilefor</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">cooling</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000080;font-style:italic;">/*t*/</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">temp</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">0.07</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">temp</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">analytic</span><span style="color: #0000FF;">()</span>▼
<span style="color: #000000;">ivp_euler</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">coolinga</span> <span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100analytic</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">e2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ivp_euler</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cooling</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">52</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">e5</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ivp_euler</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cooling</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">105</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">e10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ivp_euler</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cooling</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span>
▲ <span style="color: #0080807060A8;">forprintf</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=(</span> <span style="color: #000000;">01</span> <span style="color: #0080800000FF;">to,</span> <span style="color: #000000008000;">100</span>" <span style="color: #008080;">by</span> <span style="colorTime: #000000; %s\n">10</span> <span style="color: #0080800000FF;">do,{</span> <span style="color: #7060A8;">printfjoin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1x</span><span style="color: #0000FF;">,</span><span style="color: #008000000000;">" %7g"fmt</span><span style="color: #0000FF;">,</span> <span style:="color: #000000;">t</span><span style="color: #0000FF008000;">)</span> <span style="color: #008080;%7d">end</span> <span style="color: #0080800000FF;">for)})</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;">"Analytic: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%7.3f"</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: #000000008000;">FMT</span><span style="color: #0000FF;">,</span>Step <span style="color2: #000000; %s\n">20</span> <span style="color: #0000FF;">+,{</span> <span style="color: #0000007060A8;">80join</span> <span style="color: #0000FF;">*(</span> <span style="color: #7060A8000000;">expe2</span><span style="color: #0000FF;">(-,</span><span style="color: #000000;">0.07fmt</span> <span style="color: #0000FF;">*:=</span> <span style="color: #000000008000;">t"%7.3f"</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;">" Step 5: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%7.3f"</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;">" Step 10: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%7.3f"</span><span style="color: #0000FF;">)})</span>
<span style="color: #000080;font-style:italic;">-- and a simple plot</span>
▲ <span style="color: #008080;">include</span> <span style="color: #000000;">tpGUI</span> <span style="color: #0000FF;">+=.</span> <span style="color: #000000;">stepe</span>
<span style="color: #008080;">include</span> <span style="color: #7060A8;">IupGraph</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
▲ <span style="color: #7060A8008080;">printffunction</span> <span style="color: #0000FF000000;">(get_data</span><span style="color: #0000000000FF;">1(</span><span style="color: #0000FF004080;">,Ihandle</span> <span style="color: #008000000080;">"\nAnalyticfont-style: italic;">/*graph*/</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #008000;">"NAMES"</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"analytical"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h=2"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h=5"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h=10"</span><span style="color: #0000FF;">}},</span>
▲ <span style="color: #0000FF;">{</span><span style="color: #008080000000;">ifx</span><span style="color: #0000FF;">,</span><span style="color: #7060A8000000;">remaindera</span><span style="color: #0000FF;">(,</span><span style="color: #000000004600;">tCD_BLUE</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10x</span><span style="color: #0000FF;">)==,</span><span style="color: #000000;">0e2</span> <span style="color: #0080800000FF;">then,</span> <span style="color: #7060A8004600;">printfCD_GREEN</span><span style="color: #0000FF;">(},{</span><span style="color: #000000;">1x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">FMTe5</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_BLACK</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">yx</span><span style="color: #0000FF;">),</span><span style="color: #000000;">e10</span><span style="color: #0080800000FF;">end,</span><span style="color: #004600;">CD_RED</span><span style="color: #0080800000FF;">if}}</span>
▲ <span style="color: #008080;">end</span> <span style="color: #008080;">procedurefunction</span>
▲ <span style="color: #0000007060A8;">analyticIupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_data</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`RASTERSIZE=340x240,GRID=NO`</span><span style="color: #0000FF;">)</span>
▲ <span style="color: #7060A8;">printfIupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1graph</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">" Time: "`XTICK=20,XMIN=0,XMAX=100,XMARGIN=25`</span><span style="color: #0000FF;">)</span>
▲ <span style="color: #7060A8;">printfIupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1graph</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"\n"`YTICK=20,YMIN=20,YMAX=100`</span><span style="color: #0000FF;">)</span>
▲ <span style="color: #7060A8;">printfIupShow</span><span style="color: #0000FF;">(</span><span style="color: #0000007060A8;">1IupDialog</span><span style="color: #0000FF;">,(</span> <span style="color: #008000000000;">" Step %2d: "graph</span><span style="color: #0000FF;">,</span> <span style="color: #000000008000;">step`TITLE="Euler Method",MINSIZE=260x200`</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</lang>-->
{{out}}
Petelomax
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