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<title>ImplicitEuler&lt; Operator &gt; Class Template Reference</title>
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<div class="title">ImplicitEuler&lt; Operator &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__findiff.html">Finite-differences framework</a></div></div>  </div>
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<!-- doxytag: class="QuantLib::ImplicitEuler" --><!-- doxytag: inherits="QuantLib::MixedScheme" -->
<p>Backward Euler scheme for finite difference methods.  
 <a href="class_quant_lib_1_1_implicit_euler.html#details">More...</a></p>

<p><code>#include &lt;ql/methods/finitedifferences/impliciteuler.hpp&gt;</code></p>
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Inheritance diagram for ImplicitEuler&lt; Operator &gt;:</div>
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<div class="center"><img src="class_quant_lib_1_1_implicit_euler__inherit__graph.png" border="0" usemap="#_implicit_euler_3_01_operator_01_4_inherit__map" alt="Inheritance graph"/></div>
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<p><a href="class_quant_lib_1_1_implicit_euler-members.html">List of all members.</a></p>
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<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab85b62c5cc90bded0075d322e91fd993"></a><!-- doxytag: member="QuantLib::ImplicitEuler::traits" ref="ab85b62c5cc90bded0075d322e91fd993" args="" -->
typedef OperatorTraits&lt; Operator &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>traits</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a02ede700df8d04acf392294f6ab090c4"></a><!-- doxytag: member="QuantLib::ImplicitEuler::operator_type" ref="a02ede700df8d04acf392294f6ab090c4" args="" -->
typedef traits::operator_type&#160;</td><td class="memItemRight" valign="bottom"><b>operator_type</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac07e755f1412353806d561469c9ad49f"></a><!-- doxytag: member="QuantLib::ImplicitEuler::array_type" ref="ac07e755f1412353806d561469c9ad49f" args="" -->
typedef traits::array_type&#160;</td><td class="memItemRight" valign="bottom"><b>array_type</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7fb68e182d263712988c9b0afe1ad6a0"></a><!-- doxytag: member="QuantLib::ImplicitEuler::bc_set" ref="a7fb68e182d263712988c9b0afe1ad6a0" args="" -->
typedef traits::bc_set&#160;</td><td class="memItemRight" valign="bottom"><b>bc_set</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9b68be7f0b8097f723468a930f604c39"></a><!-- doxytag: member="QuantLib::ImplicitEuler::condition_type" ref="a9b68be7f0b8097f723468a930f604c39" args="" -->
typedef <a class="el" href="class_quant_lib_1_1_step_condition.html">traits::condition_type</a>&#160;</td><td class="memItemRight" valign="bottom"><b>condition_type</b></td></tr>
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Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9d3488329720367c427f836b019924cf"></a><!-- doxytag: member="QuantLib::ImplicitEuler::ImplicitEuler" ref="a9d3488329720367c427f836b019924cf" args="(const operator_type &amp;L, const bc_set &amp;bcs)" -->
&#160;</td><td class="memItemRight" valign="bottom"><b>ImplicitEuler</b> (const operator_type &amp;L, const bc_set &amp;bcs)</td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template&lt;class Operator&gt;<br/>
class QuantLib::ImplicitEuler&lt; Operator &gt;</h3>

<p>Backward Euler scheme for finite difference methods. </p>
<p>In this implementation, the passed operator must be derived from either TimeConstantOperator or TimeDependentOperator. Also, it must implement at least the following interface:</p>
<div class="fragment"><pre class="fragment">        <span class="keyword">typedef</span> ... array_type;

        <span class="comment">// copy constructor/assignment</span>
        <span class="comment">// (these will be provided by the compiler if none is defined)</span>
        Operator(<span class="keyword">const</span> Operator&amp;);
        Operator&amp; operator=(<span class="keyword">const</span> Operator&amp;);

        <span class="comment">// inspectors</span>
        <a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> size();

        <span class="comment">// modifiers</span>
        <span class="keywordtype">void</span> setTime(<a class="code" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7" title="continuous quantity with 1-year units">Time</a> t);

        <span class="comment">// operator interface</span>
        array_type solveFor(<span class="keyword">const</span> array_type&amp;);
        <span class="keyword">static</span> Operator identity(<a class="code" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77" title="size of a container">Size</a> size);

        <span class="comment">// operator algebra</span>
        Operator operator*(<a class="code" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78" title="real number">Real</a>, <span class="keyword">const</span> Operator&amp;);
        Operator operator+(<span class="keyword">const</span> Operator&amp;, <span class="keyword">const</span> Operator&amp;);
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