celeritas::RungeKuttaIntegrator< EquationT > Class Template Reference

Integrate the field ODEs using the 4th order classical Runge-Kutta method. More...

#include <RungeKuttaIntegrator.hh>

Public Types
Type aliases
using	result_type = FieldIntegration

Public Member Functions
CELER_FUNCTION	RungeKuttaIntegrator (EquationT &&eq)
	Construct with the equation of motion.
CELER_FUNCTION result_type	operator() (real_type step, OdeState const &beg_state) const
	Numerically integrate and return the updated state with estimated error.

Detailed Description

template<class EquationT>
class celeritas::RungeKuttaIntegrator< EquationT >

Integrate the field ODEs using the 4th order classical Runge-Kutta method.

This method estimates the updated state from an initial state and evaluates the truncation error, with fourth-order accuracy based on description in Numerical Recipes in C, The Art of Scientific Computing, Sec. 16.2, Adaptive Stepsize Control for Runge-Kutta.

For a magnetic field equation f along a charged particle trajectory with state y, which includes position and momentum but may also include time and spin. For N-variables (i = 1, ... N), the right hand side of the equation

\[ \difd{y_{i}}{s} = f_i (s, y_{i}) \]

and the fouth order Runge-Kutta solution for a given step size, h is

\[ y_{n+1} - y_{n} = h f(x_n, y_n) = \frac{h}{6} (k_1 + 2 k_2 + 2 k_3 + k_4) \]

which is the average slope at four different points. The truncation error is the difference of the final states of one full step (y1) and two half steps (y2)

\[ \Delta = y_2 - y_1, y(x+h) = y_2 + \frac{\Delta}{15} + \mathrm{O}(h^{6}) \]

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The documentation for this class was generated from the following file:

• RungeKuttaIntegrator.hh