Merge commit '4ebe6417a5fce5f0994fc0c31bebf732be96a07c' as 'boost'

boost/libs/numeric/odeint/examples/simple1d.cpp

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+/* Boost libs/numeric/odeint/examples/simple1d.cpp
+
+ Copyright 2012-2013 Mario Mulansky
+ Copyright 2012 Karsten Ahnert
+
+ example for a simple one-dimensional 1st order ODE
+
+ Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE_1_0.txt or
+ copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+
+#include <iostream>
+#include <boost/numeric/odeint.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+
+/* we solve the simple ODE x' = 3/(2t^2) + x/(2t)
+ * with initial condition x(1) = 0.
+ * Analytic solution is x(t) = sqrt(t) - 1/t
+ */
+
+void rhs( const double x , double &dxdt , const double t )
+{
+    dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
+}
+
+void write_cout( const double &x , const double t )
+{
+    cout << t << '\t' << x << endl;
+}
+
+// state_type = double
+typedef runge_kutta_dopri5< double > stepper_type;
+
+int main()
+{
+    double x = 0.0; //initial value x(1) = 0
+    // use dopri5 with stepsize control and allowed errors 10^-12, integrate t=1...10
+    integrate_adaptive( make_controlled( 1E-12 , 1E-12 , stepper_type() ) , rhs , x , 1.0 , 10.0 , 0.1 , write_cout );
+}