Schema_RK_Williamson.h

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#ifndef Schema_RK_Williamson_included
#define Schema_RK_Williamson_included
 
#include <TRUSTSchema_RK.h>
 
/// \cond DO_NOT_DOCUMENT
class Schema_RK_Williamson
{ };
/// \endcond
 
/*! @brief : class RK2 This class represents a second-order Runge-Kutta time scheme, case 1 of Williamson, written as:
 *
 *      q1=h f(x0)
 *      x1=x0+b1 q1
 *      q2=h f(x1) +a2 q1
 *      x2=x1+b2 q2, avec a1=0, a2=sqrt(2)-2, b1=sqrt(2)/2, b2=sqrt(2)/2
 *
 */
class RK2: public TRUSTSchema_RK<Ordre_RK::DEUX_WILLIAMSON>
{
  Declare_instanciable(RK2);
};
 
 
/*! @brief : class RK3 This class represents a third-order Runge-Kutta time scheme, case 7 of Williamson, written as:
 *
 *      q1=h f(x0)
 *      x1=x0+b1 q1
 *      q2=h f(x1) +a2 q1
 *      x2=x1+b2 q2
 *      q3=h f(x2)+a3 q2
 *      x3=x2+b3 q3, avec a1=0, a2=-5/9, a3=-153/128, b1=1/3, b2=15/16, b3=8/15
 *
 */
class RK3: public TRUSTSchema_RK<Ordre_RK::TROIS_WILLIAMSON>
{
  Declare_instanciable(RK3);
};
 
/*! @brief : class RK4 This class represents a degenerate fourth-order Runge-Kutta time scheme (three-point scheme), case 17 of Williamson, written as:
 *
 *      q1=h f(x0)
 *      x1=x0+b1 q1
 *      q2=h f(x1) +a2 q1
 *      x2=x1+b2 q2
 *      q3=h f(x2)+a3 q2
 *      x3=x2+b3 q3, avec a1=0, a2=-1/2, a3=-2, b1=1/2, b2=1, b3=1/6
 *
 */
class RK4: public TRUSTSchema_RK<Ordre_RK::QUATRE_WILLIAMSON>
{
  Declare_instanciable(RK4);
};
 
#endif /* Schema_RK_Williamson_included */