runge-kutta.h File Reference

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Functions
static double	update (scalar *ul, scalar *kl, double t, double dt, void(*Lu)(scalar *ul, double t, scalar *kl), scalar *dul, double w)
void	runge_kutta (scalar *ul, double t, double dt, void(*Lu)(scalar *ul, double t, scalar *kl), int order)
	The runge_kutta() function implements the classical first- (Euler), second- and fourth-order Runge–Kutta time integrators for evolution equations of the form.

Function Documentation

runge_kutta()

void runge_kutta	(	scalar *	ul,
		double	t,
		double	dt,
		void(*)(scalar *ul, double t, scalar *kl)	Lu,
		int	order
	)

The runge_kutta() function implements the classical first- (Euler), second- and fourth-order Runge–Kutta time integrators for evolution equations of the form.

\[ \frac{\partial\mathbf{u}}{\partial t} = L(\mathbf{u}, t) \]

with \(\mathbf{u}\) a vector (i.e. list) of evolving fields and \(L()\) a generic, user-defined operator.

Given \(\mathbf{u}\), the initial time t, a timestep dt and the function \(L()\) which should fill kl with the right-hand-side of the evolution equation, the function below will return \(\mathbf{u}\) at time \(t + dt\) using the Runge–Kutta scheme specified by order.

Definition at line 42 of file runge-kutta.h.

References _i, assert, dt, free(), k, list_clone(), t, u, ul, update, w, and x.

Referenced by run().

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update()

static double update ( scalar *  ul, scalar *  kl, double  t, double  dt, void(*)(scalar *ul, double t, scalar *kl)  Lu, scalar *  dul, double  w  )

static

Runge–Kutta time integrators

Definition at line 7 of file runge-kutta.h.

References _i, dt, free(), k, list_clone(), t, u, ul, w, and x.

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