runge_kutta.h File Reference

Runge-Kutta explicit ODE-integrators. More...

#include <cassert>
#include <array>
#include <tuple>
#include "ode.h"
#include "backend/exceptions.h"
#include "tableau.h"
#include "blas1.h"
#include "implicit.h"

Go to the source code of this file.

Classes
struct	dg::IdentityFilter
	A filter that does nothing. More...
struct	dg::ERKStep< ContainerType >
	Embedded Runge Kutta explicit time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \\ \tilde u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s \tilde b_j k_j \\ \delta^{n+1} = u^{n+1} - \tilde u^{n+1} = \Delta t\sum_{j=1}^s (b_j - \tilde b_j) k_j \end{align} \). More...
struct	dg::FilteredERKStep< ContainerType >
	EXPERIMENTAL: Filtered Embedded Runge Kutta explicit time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, \Lambda\Pi \left[u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right]\right) \\ u^{n+1} = \Lambda\Pi\left[u^{n} + \Delta t\sum_{j=1}^s b_j k_j\right] \\ \delta^{n+1} = \Delta t\sum_{j=1}^s (\tilde b_j - b_j) k_j \end{align} \). More...
struct	dg::ARKStep< ContainerType >
	Additive Runge Kutta (semi-implicit) time-step with error estimate following The ARKode library More...
struct	dg::DIRKStep< ContainerType >
	Embedded diagonally implicit Runge Kutta time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \\ \tilde u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s \tilde b_j k_j \\ \delta^{n+1} = u^{n+1} - \tilde u^{n+1} = \Delta t\sum_{j=1}^s (b_j-\tilde b_j) k_j \end{align} \). More...
struct	dg::ShuOsher< ContainerType >
	Shu-Osher fixed-step explicit ODE integrator with Slope Limiter / Filter \( \begin{align} u_0 &= u_n \\ u_i &= \Lambda\Pi \left(\sum_{j=0}^{i-1}\left[ \alpha_{ij} u_j + \Delta t \beta_{ij} f( t_j, u_j)\right]\right)\\ u^{n+1} &= u_s \end{align} \). More...
struct	dg::SinglestepTimeloop< ContainerType >
	Integrate using a for loop and a fixed time-step. More...

Namespaces
namespace	dg
	This is the namespace for all functions and classes defined and used by the discontinuous Galerkin library.

Typedefs
template<class ContainerType >
using	dg::RungeKutta = ERKStep<ContainerType>
	Runge-Kutta fixed-step explicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \end{align} \).
template<class ContainerType >
using	dg::FilteredRungeKutta = FilteredERKStep<ContainerType>
	Filtered Runge-Kutta fixed-step explicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, \Lambda\Pi \left[u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right]\right) \\ u^{n+1} = \Lambda\Pi\left[u^{n} + \Delta t\sum_{j=1}^s b_j k_j\right] \end{align} \).
template<class ContainerType >
using	dg::ImplicitRungeKutta = DIRKStep<ContainerType>
	Runge-Kutta fixed-step implicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{s} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \end{align} \).

Functions
bool	dg::is_same (double x, double y, double eps=1e-15)
bool	dg::is_same (float x, float y, float eps=1e-6)
template<class T >
bool	dg::is_same (T x, T y)
bool	dg::is_divisable (double a, double b, double eps=1e-15)
bool	dg::is_divisable (float a, float b, float eps=1e-6)

Detailed Description

Runge-Kutta explicit ODE-integrators.