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5155 changed files with 53816 additions and 36252 deletions
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17
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation" target="_blank">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method" target="_blank">semi implicit Euler method</a> </p>
<dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<p>The ODE being solved is: </p><p class="formulaDsp">
<p>The ODE being solved is: </p><p class="formulaDsp">
\begin{eqnarray*}
\dot{u} &amp;=&amp; v\\
\dot{v} &amp;=&amp; -\omega^2 u\\
\omega &amp;=&amp; 1\\
[x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)}
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\dot{u} &amp;=&amp; v\\
\dot{v} &amp;=&amp; -\omega^2 u\\
\omega &amp;=&amp; 1\\
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<p> The exact solution for the above problem is: </p><p class="formulaDsp">
<p> The exact solution for the above problem is: </p><p class="formulaDsp">
\begin{eqnarray*}
u(x) &amp;=&amp; \cos(x)\\
v(x) &amp;=&amp; -\sin(x)\\
\end{eqnarray*}
u(x) &amp;=&amp; \cos(x)\\
v(x) &amp;=&amp; -\sin(x)\\
\end{eqnarray*}
</p>
<p> The computation results are stored to a text file <code>semi_implicit_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_semi_implicit_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
<p>To implement <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator" target="_blank">Van der Pol oscillator</a>, change the <a class="el" href="#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> function to: </p><div class="fragment"><div class="line"><span class="keyword">const</span> <span class="keywordtype">double</span> mu = 2.0;</div>
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<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"></span></td><td>)</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
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@@ -3,7 +3,7 @@
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.10.0"/>
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<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
@@ -11,9 +11,9 @@
<script type="text/javascript" src="../../dynsections.js"></script>
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
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<td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a> * dequeue </td>
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<td class="memname">void Insert </td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td class="memname">void Remove </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *</td> <td class="paramname"><span class="paramname"><em>p</em>, </span></td>
<td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *</td> <td class="paramname"><span class="paramname"><em>p</em></span>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *</td> <td class="paramname"><span class="paramname"><em>n</em>, </span></td>
<td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *</td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
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@@ -11,9 +11,9 @@
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@@ -43,18 +43,23 @@ MathJax.Hub.Config({
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<script type="text/javascript">
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initMenu('../../',true,false,'search.php','Search',true);
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<div id="doc-content">
@@ -210,13 +215,11 @@ Private Attributes</h2></td></tr>
<div class="line"><span class="lineno"> 143</span> <span class="comment">// and also no prefix in the line</span></div>
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">while</span> (!(nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;word_end) &amp;&amp; nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;children.empty()) {</div>
<div class="line"><span class="lineno"> 145</span> nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/pop.html">pop</a>();</div>
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<div class="line"><span class="lineno"> 147</span> word.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">pop_back</a>();</div>
<div class="line"><span class="lineno"> 146</span> nodes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack/top.html">top</a>()-&gt;children.erase(word.back());</div>
<div class="line"><span class="lineno"> 147</span> word.pop_back();</div>
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<div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/back.html">std::string::back</a></div><div class="ttdeci">T back(T... args)</div></div>
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<div class="ttc" id="apop_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">std::string::pop_back</a></div><div class="ttdeci">T pop_back(T... args)</div></div>
<div class="ttc" id="apop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack/pop.html">std::stack::pop</a></div><div class="ttdeci">T pop(T... args)</div></div>
<div class="ttc" id="apush_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack/push.html">std::stack::push</a></div><div class="ttdeci">T push(T... args)</div></div>
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@@ -242,12 +245,12 @@ Here is the call graph for this function:</div>
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt; data_structures::trie_using_hashmap::Trie::get_all_words </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt;</td> <td class="paramname"><span class="paramname"><em>results</em>, </span></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt;</td> <td class="paramname"><span class="paramname"><em>results</em></span>, </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html">Node</a> &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>element</em>, </span></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html">Node</a> &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>element</em></span>, </td>
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<div class="line"><span class="lineno"> 170</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> key = <span class="stringliteral">&quot;&quot;</span>;</div>
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<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="aclassdata__structures_1_1trie__using__hashmap_1_1_trie_html_a7bbe538c8015e8ce158e7ed43f605ebd"><div class="ttname"><a href="#a7bbe538c8015e8ce158e7ed43f605ebd">data_structures::trie_using_hashmap::Trie::get_all_words</a></div><div class="ttdeci">std::vector&lt; std::string &gt; get_all_words(std::vector&lt; std::string &gt; results, const std::shared_ptr&lt; Node &gt; &amp;element, std::string prefix)</div><div class="ttdoc">helper function to predict/recommend words that starts with a given prefix from the end of prefix's n...</div><div class="ttdef"><b>Definition</b> trie_using_hashmap.cpp:160</div></div>
<div class="ttc" id="apop_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/pop_back.html">std::string::pop_back</a></div><div class="ttdeci">T pop_back(T... args)</div></div>
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Namespaces</h2></td></tr>
<tr class="memitem:d6/d4e/namespaceciphers" id="r_d6/d4e/namespaceciphers"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d4e/namespaceciphers.html">ciphers</a></td></tr>
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<tr class="memdesc:d6/d4e/namespaceciphers"><td class="mdescLeft">&#160;</td><td class="mdescRight">Algorithms for encryption and decryption. <br /></td></tr>
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<tr class="memitem:d7/d47/namespace_x_o_r" id="r_d7/d47/namespace_x_o_r"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d47/namespace_x_o_r.html">XOR</a></td></tr>
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<tr class="memdesc:d7/d47/namespace_x_o_r"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm. <br /></td></tr>
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