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Updated toolbox documentation and README, added option to open toolbo…
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Expand Up @@ -8,6 +8,23 @@ Collection of fixed-step ODE solvers, functions to generate ODE solver equations
[Toolbox Documentation](https://tamaskis.github.io/ODE_Solver_Toolbox-MATLAB/)\
[Technical Documentation](https://tamaskis.github.io/documentation/Fixed_Step_ODE_Solvers.pdf)

To open the home page of the toolbox documentation in MATLAB, type

```
doc_OST
```

in the Command Window. To open the documentation of a specific function with name `function_name` from the Command Window, type

```
doc_OST function_name
```

To open the PDF file with the technical documentation (Fixed_Step_ODE_Solvers.pdf) from the Command Window, type

```
doc_OST tech
```

## Explicit Runge-Kutta (Single-Step) Methods

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</pre><pre class="codeoutput">
y10 =

0.002270005950239
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB2_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB2_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB2_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB2(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

50.000000249970483
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB2_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB2_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB2_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272275954297
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
##### SOURCE BEGIN #####
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<!--
This HTML was auto-generated from MATLAB code.
To make changes, update the MATLAB code and republish this document.
--><title>AB3</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-22"><meta name="DC.source" content="AB3_doc.m"><style type="text/css">
--><title>AB3</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-29"><meta name="DC.source" content="AB3_doc.m"><style type="text/css">
html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}

html { min-height:100%; margin-bottom:1px; }
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</pre><pre class="codeoutput">
y10 =

0.002269996479605
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB3_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB3_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB3_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB3(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

49.999999625112032
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB3_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB3_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB3_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272266476087
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
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<!--
This HTML was auto-generated from MATLAB code.
To make changes, update the MATLAB code and republish this document.
--><title>AB4</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-22"><meta name="DC.source" content="AB4_doc.m"><style type="text/css">
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html { min-height:100%; margin-bottom:1px; }
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</pre><pre class="codeoutput">
y10 =

0.002269996488132
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB4_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB4_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB4_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB4(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

50.000000000000924
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB4_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB4_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB4_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272266484620
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
##### SOURCE BEGIN #####
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<!--
This HTML was auto-generated from MATLAB code.
To make changes, update the MATLAB code and republish this document.
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html { min-height:100%; margin-bottom:1px; }
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</pre><pre class="codeoutput">
y10 =

0.002269996488124
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB5_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB5_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB5_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB5(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

49.999999999999496
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB5_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB5_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB5_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272266484612
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
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<!--
This HTML was auto-generated from MATLAB code.
To make changes, update the MATLAB code and republish this document.
--><title>AB6</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-22"><meta name="DC.source" content="AB6_doc.m"><style type="text/css">
--><title>AB6</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-29"><meta name="DC.source" content="AB6_doc.m"><style type="text/css">
html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}

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</pre><pre class="codeoutput">
y10 =

0.002269996488124
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB6_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB6_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB6_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB6(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

50.000000000000043
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB6_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB6_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB6_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272266484612
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
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This HTML was auto-generated from MATLAB code.
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--><title>AB7</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-22"><meta name="DC.source" content="AB7_doc.m"><style type="text/css">
--><title>AB7</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-12-29"><meta name="DC.source" content="AB7_doc.m"><style type="text/css">
html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}

html { min-height:100%; margin-bottom:1px; }
Expand Down Expand Up @@ -178,14 +178,14 @@
</pre><pre class="codeoutput">
y10 =

0.002269996488124
0.0023

</pre><p>Confirming our result by solving the same ODE but from <img src="AB7_doc_eq08325516970591449802.png" alt="$t=10$" style="width:29px;height:8px;"> to <img src="AB7_doc_eq01961946856973312452.png" alt="$t=20$" style="width:29px;height:8px;"> and using our result for <img src="AB7_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> as the initial condition,</p><pre class="codeinput">[t,y] = AB7(f,[10,20],y10,0.001);
y20 = y(end)
</pre><pre class="codeoutput">
y20 =

50.000000000000092
50.0000

</pre><h2 id="18">Example #4: Backward integration (event-detection case).</h2><p><i>Once again, consider</i></p><p><img src="AB7_doc_eq15707102448259949290.png" alt="$$\frac{dy}{dt}=y,\quad y(20)=50$$" style="width:100px;height:23px;"></p><p><i>Find <img src="AB7_doc_eq14770085807156189371.png" alt="$y(10)$" style="width:25px;height:11px;"> using an ODE solver with a condition function (i.e. event-detection).</i></p><p>First, let's define our ODE (<img src="AB7_doc_eq15749537601348477239.png" alt="$\frac{dy}{dt}=f(t,y)$" style="width:53px;height:15px;">) and initial condition in MATLAB.</p><pre class="codeinput">f = @(t,y) y;
y20 = 50;
Expand All @@ -195,7 +195,7 @@
</pre><pre class="codeoutput">
y10 =

0.002272266484612
0.0023

</pre><p>Note that this is the same result we obtained earlier in Example #3.</p><h2 id="23">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
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