TNL::Solvers::ODE Namespace Reference

Namespace for solvers of ordinary differential equations. More...

Classes
class	Euler
	Solver of ODEs with the first order of accuracy. More...
class	ExplicitSolver
	Base class for ODE solvers and explicit solvers od PDEs. More...
class	Merson
	Solver of ODEs with the first order of accuracy. More...
class	StaticEuler
	Solver of ODEs with the first order of accuracy. More...
class	StaticEuler< Containers::StaticVector< Size_, Real > >
	Solver of ODEs with the first order of accuracy. More...
class	StaticExplicitSolver
	Base class for ODE solvers and explicit solvers od PDEs. More...
class	StaticMerson
	Solver of ODEs with the first order of accuracy. More...
class	StaticMerson< Containers::StaticVector< Size_, Real > >
	Solver of ODEs with the first order of accuracy. More...

Detailed Description

Namespace for solvers of ordinary differential equations.

Solvers in this namespace represent numerical methods for the solution of the ordinary differential equations of the following form:

\[ \frac{d \vec u}{dt} = \vec f( t, \vec u)\ \rm{ on }\ (0,T) \]

\[ \vec u( 0 ) = \vec u_{ini}. \]

The following solvers are available:

1. First order of accuracy a. TNL::Solvers::ODE::StaticEuler, TNL::Solvers::ODE::Euler - the Euler method
2. Fourth order of accuracy a. TNL::Solvers::ODE::StaticMerson, TNL::Solvers::ODE::Merson - the Runge-Kutta-Merson method with adaptive choice of the time step.

The static variants of the solvers are supposed to be used when the unknown \( x \in R^n \) is expressed by a Containers::StaticVector or it is a scalar, i.e. \( x \in R \) expressed by a numeric type like double or float.