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@@ -119,9 +119,9 @@ Functions</h2></td></tr>
<tr class="memitem:af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y)</td></tr>
<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exact solution of the problem. Used for solution comparison. <a href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">More...</a><br /></td></tr>
<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
<tr class="memdesc:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the forward-Euler method. <a href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">More...</a><br /></td></tr>
<tr class="separator:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a> (const double dx, const double x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
<tr class="memdesc:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the forward-Euler method. <a href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">More...</a><br /></td></tr>
<tr class="separator:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
<tr class="memdesc:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the forward-Euler method in the given limits. <a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">More...</a><br /></td></tr>
<tr class="separator:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
@@ -218,29 +218,29 @@ Here is the call graph for this function:</div>
</table>
</div><div class="memdoc">
<p>Main Function </p>
<div class="fragment"><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; {</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <span class="keywordtype">double</span> X0 = 0.f; <span class="comment">/* initial value of x0 */</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; <span class="keywordtype">double</span> X_MAX = 10.F; <span class="comment">/* upper limit of integration */</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> Y0 = {1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; <span class="keywordtype">double</span> step_size;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; <span class="keywordflow">if</span> (argc == 1) {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the step size: &quot;</span>;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; step_size;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; <span class="comment">// use commandline argument as independent variable step size</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; step_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; }</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; </div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; <span class="comment">// get approximate solution</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; <span class="keywordtype">double</span> total_time = <a class="code" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a>(step_size, X0, X_MAX, &amp;Y0, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; <span class="comment">/* compute exact solution for comparion */</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(X0, X_MAX, step_size, Y0);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; {</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; <span class="keywordtype">double</span> X0 = 0.f; <span class="comment">/* initial value of x0 */</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <span class="keywordtype">double</span> X_MAX = 10.F; <span class="comment">/* upper limit of integration */</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> Y0{1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; <span class="keywordtype">double</span> step_size = NAN;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; <span class="keywordflow">if</span> (argc == 1) {</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the step size: &quot;</span>;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; step_size;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <span class="comment">// use commandline argument as independent variable step size</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; step_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; }</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; <span class="comment">// get approximate solution</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; <span class="keywordtype">double</span> total_time = <a class="code" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a>(step_size, X0, X_MAX, &amp;Y0, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; </div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <span class="comment">/* compute exact solution for comparion */</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(X0, X_MAX, step_size, Y0);</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;}</div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
@@ -294,8 +294,8 @@ Here is the call graph for this function:</div>
</dl>
<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> omega = 1.F; <span class="comment">// some const for the problem</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; dy[0][0] = y[0][1]; <span class="comment">// x dot</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; dy[0][1] = -omega * omega * y[0][0]; <span class="comment">// y dot</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; (*dy)[0] = (*y)[1]; <span class="comment">// x dot // NOLINT</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; (*dy)[1] = -omega * omega * (*y)[0]; <span class="comment">// y dot // NOLINT</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;}</div>
</div><!-- fragment -->
</div>
@@ -347,36 +347,36 @@ Here is the call graph for this function:</div>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160; {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="keywordtype">double</span> x = X0;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> y = Y0;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">&quot;exact.csv&quot;</span>, std::ostream::out);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; <span class="keywordflow">if</span> (!fp.is_open()) {</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; }</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Finding exact solution\n&quot;</span>;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; y.size() - 1; i++) {</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; fp &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; fp &lt;&lt; y[y.size() - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(x, &amp;y);</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; x += step_size;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; } <span class="keywordflow">while</span> (x &lt;= X_MAX);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordtype">double</span> total_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; fp.close();</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; {</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; <span class="keywordtype">double</span> x = X0;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> y(Y0);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">&quot;exact.csv&quot;</span>, std::ostream::out);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <span class="keywordflow">if</span> (!fp.is_open()) {</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; }</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Finding exact solution\n&quot;</span>;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; y.size() - 1; i++) {</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; fp &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>; <span class="comment">// NOLINT</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; }</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; fp &lt;&lt; y[y.size() - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>; <span class="comment">// NOLINT</span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(x, &amp;y);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; x += step_size;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; } <span class="keywordflow">while</span> (x &lt;= X_MAX);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <span class="keywordtype">double</span> total_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; fp.close();</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;}</div>
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<div class="ttc" id="aode__forward__euler_8cpp_html_af3adf7b092a87868917ee5fb4255192b"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a></div><div class="ttdeci">void exact_solution(const double &amp;x, std::valarray&lt; double &gt; *y)</div><div class="ttdoc">Exact solution of the problem. Used for solution comparison.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:67</div></div>
<div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:152</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:153</div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>