ODE_IVP.h

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/// \file ODE_IVP.h
/// A specification for a class to solve initial value problems of the form
/// \f[ \underline{ \dot f} (t) = \underline R ( \underline f (t), t) \,, \f]
/// where \f$ \underline f (0) \f$ is known.
 
#ifndef ODE_IVP_H
#define ODE_IVP_H
 
#include <Types.h>
#include <Equation.h>
#include <OneD_Node_Mesh.h>
#include <Uncopyable.h>
 
namespace CppNoddy {
 
  /// A templated object for real/complex vector system
  /// of first-order ordinary differential equations.
 
  template <typename _Type>
  class ODE_IVP : private Uncopyable {
   public:
 
    /// The class is defined by a vector function for the system.
    /// \param equation_ptr A pointer to an inherited Equation object.
    /// \param x_init The starting point of the domain for the ODE.
    /// \param x_final The end point of the domain for the ODE.
    /// \param num_of_steps A maximum/default number of steps to be taken.
    ODE_IVP(Equation<_Type > *equation_ptr,
            const double &x_init,
            const double &x_final,
            const std::size_t &num_of_steps);
 
    ~ODE_IVP();
 
    /// A fixed step 4th order Runge-Kutta method.
    /// \param u An NVector of initial values.
    /// \return An NVector of the final values.
    DenseVector<_Type> shoot4(DenseVector<_Type> u);
 
    /// A Runge-Kutta-Fehlberg integrator.
    /// \param u An Nvector of initial values.
    /// \param tol The tolerance used in choosing the step length.
    /// \param h_init The initial step length.
    /// \return An NVector of the final values.
    DenseVector<_Type> shoot45(DenseVector<_Type> u, const double& tol, const double& h_init);
 
    /// Return the history of the stepped solution.
    /// \return A reference to the mesh solution
    OneD_Node_Mesh<_Type>& get_mesh();
 
    /// Return a handle to the STORE_EVERY object
    /// \return A reference to the STORE_EVERY variable
    unsigned& store_every();
    
   private:
 
    /// initial and final step points
    double X_INIT, X_FINAL;
    /// initial step size
    double H_INIT;
    /// maximum number of steps to take
    std::size_t N;
    /// The function associated with this instance.
    Equation<_Type > *p_EQUATION;
    /// Store every
    unsigned STORE_EVERY;
    /// In-class storage of the solution
    OneD_Node_Mesh<_Type> SOLN;
  }
  ; // end class
 
 
} // end namespace
 
 
#endif