Explicit 5/4 pair, also with 3rd, 2nd, and 1st order embedded methods, from Cash & Karp. More...

#include <ode_rkck.h>

Inheritance diagram for ode::OdeRKCK:

Public Member Functions
	OdeRKCK (unsigned long neq)
	constructs

Public Member Functions inherited from ode::OdeEmbedded
	OdeEmbedded (unsigned long neq, bool need_jac, int lowerord)
	constructs

virtual	~OdeEmbedded ()
	destructs

double	get_facsafe ()
	gets safety factor applied to time step selection

double	get_facmin ()
	gets minimum allowable fraction change in time step (a number <1)

double	get_facmax ()
	gets maximum allowable fraction change in time step (a number >1)

void	set_facsafe (double facsafe)
	sets safety factor applied to time step selection

void	set_facmin (double facmin)
	sets minimum allowable fraction change in time step (a number <1)

void	set_facmax (double facmax)
	sets maximum allowable fraction change in time step (a number >1)

Public Member Functions inherited from ode::OdeAdaptive
	OdeAdaptive (unsigned long neq, bool need_jac)
	constructs

virtual	~OdeAdaptive ()
	destructs

long unsigned	get_nrej ()
	gets the count of rejected steps

double	get_abstol ()
	gets the absolute error tolerance

double	get_reltol ()
	gets the relative error tolerance

double	get_dtmax ()
	gets the maximum allowable time step

void	set_abstol (double tol)
	sets the absolute error tolerance

void	set_reltol (double tol)
	sets the relative error tolerance

void	set_tol (double tol)
	sets the absolute and relative error tolerance to the same value

void	set_dtmax (double dtmax)
	sets the maximum allowable time step

void	solve_adaptive (double tint, double dt0, bool extras=true)
	integrates for a specified duration of independent variable without output

void	solve_adaptive (double tint, double dt0, const char *dirout, int inter)
	lots of output, solves and stores every "inter" point along the way

void	solve_adaptive (double tint, double dt0, unsigned long nsnap, const char *dirout)
	solves and writes evenly spaced snapshots

void	solve_adaptive (double dt0, double tsnap, unsigned long nsnap, const char dirout)
	solves and writes snapshots at times specified in the tsnap array

Public Member Functions inherited from ode::OdeBase
	OdeBase (unsigned long neq, bool need_jac)
	constructs

virtual	~OdeBase ()
	destructs

const char *	get_name ()
	gets the name of the ODE system

const char *	get_method ()
	gets the name of the solver/method

const char *	get_dirout ()
	gets output directory string if one has been set

bool	get_quiet ()
	gets the boolean determining if updates are printed during solves

bool	get_silent_snap ()
	gets whether to skip writing the solution vector to file when snapping

unsigned long	get_neq ()
	gets the size of the ODE system

double	get_t ()
	gets the current value of the independent variable

double	get_dt ()
	gets the most recent or current time step size

double *	get_sol ()
	gets a pointer to the whole solution array

double	get_sol (unsigned long i)
	gets an element of the solution array

long unsigned	get_nstep ()
	gets the total number of steps taken

long unsigned	get_neval ()
	gets the total number of ODE system evaluation

long unsigned	get_icheck ()
	gets the number of steps after which the solution is checked for integrity

long unsigned	get_nJac ()
	gets the total number of Jacobian evaluations performed

void	set_t (double t)
	sets the "time," or independent variable used to track progress

void	set_sol (unsigned long i, double x)
	sets an element of the solution array

void	set_sol (double *sol)
	copies an array into the solution array

void	set_name (std::string name)
	sets the name of the ODE system

void	set_name (const char *name)
	sets the name of the ODE system

void	set_quiet (bool quiet)
	sets the boolean determining if updates are printed during solves

void	set_silent_snap (bool silent_snap)
	sets whether to skip writing the solution vector to file when snapping

void	set_icheck (unsigned long icheck)
	sets the number of steps after which the solution is checked for integrity

void	step (double dt, bool extra=true)
	increments the step counter and the time, checks the solution integrity if needed, stores the time step in the object, and executes after_step() if extra is true

void	solve_fixed (double tint, double dt, bool extras=true)
	integrates for a specified duration of independent variable without output

void	solve_fixed (double tint, double dt, const char *dirout, int inter=1)
	lots of output, solves and stores every "inter" point along the way

void	solve_fixed (double tint, double dt, unsigned long nsnap, const char *dirout)
	solves and writes evenly spaced snapshots

void	solve_fixed (double dt, double tsnap, unsigned long nsnap, const char dirout)
	solves and writes snapshots at times specified in the tsnap array

void	reset (double t, double *sol)
	reset to a specified time and initial condition array

Additional Inherited Members
Protected Member Functions inherited from ode::OdeEmbedded
double	error (double abstol, double reltol)
	calculates error estimate with lower and higher order solutions

double	facopt (double err)
	calculates factor for "optimal" next time step

virtual void	adapt (double abstol, double reltol)
	does the calculations to determine isrej and dtopt

virtual bool	is_rejected ()
	simply returns isrej

virtual double	dt_adapt ()
	simply returns dtopt

Protected Member Functions inherited from ode::OdeAdaptive
void	solve_adaptive_ (double tint, double dt0, bool extra=true)
	integrates without output or any counters, trackers, extra functions...

bool	solve_done_adaptive (double tend)
	determines whether an adaptive solve is finished

bool	step_adaptive_ (double dt, bool extra=true)
	executes a single time and calls all necessary adapting functions

double	dt_adapt_ (double tend)
	wrapper around dt_adapt() to perform additional checks

Protected Member Functions inherited from ode::OdeBase
void	solve_fixed_ (double tint, double dt, bool extra=true)
	integrates without output or any counters, trackers, extra functions...

virtual void	ode_fun (double solin, double fout)=0
	evaluates the system of ODEs in autonomous form and must be defined by a derived class

virtual void	ode_jac (double solin, double *Jout)
	evaluates the system's Jacobian matrix, also in autonomous form, and can either be defined in a derived class or left to numerical approximation

void	ode_fun_ (double solin, double fout)
	wrapper, calls ode_fun() and increases the neval counter by one

void	ode_jac_ (double solin, double *Jout)
	wrapper, calls ode_jac() and increments nJac;

virtual void	before_solve ()
	does any extra stuff before starting a solve

virtual void	after_step (double t)
	does any extra stuff after each step

virtual void	after_capture (double t)
	does any extra stuff only when a step is captured

virtual void	after_snap (std::string dirout, long isnap, double t)
	does any extra stuff after each snap

virtual void	after_solve ()
	does any extra stuff after completing a solve

void	snap (std::string dirout, long isnap, double tsnap)
	writes the current value of the solution to a binary file

bool	solve_done (double dt, double tend)
	checks if the solution is within a single time step of the end point

void	check_sol_integrity ()
	checks solution for nans and infs, exiting the program if they're found

void	check_pre_solve (double tint, double dt)
	checks that a solve can be performed with given tend and dt values

void	check_pre_snaps (double dt, double *tsnap, unsigned long nsnap)
	checks that snap times are monotonically increasing and > current time

Protected Attributes inherited from ode::OdeEmbedded
double	facsafe_
	safety factor applied to time step selection

double	facmin_
	minimum allowable fraction change in time step

double	facmax_
	maximum allowable fraction change in time step

double *	solemb_
	embedded solution array

Protected Attributes inherited from ode::OdeAdaptive
long unsigned	nrej_
	counter for rejected steps

double	abstol_
	absolute error tolerance

double	reltol_
	absolute error tolerance

double	dtmax_
	maximum allowable time step

Protected Attributes inherited from ode::OdeBase
std::string	name_
	the "name" of the system, which is used for output

std::string	method_
	the "name" of the solver/method, as in "Euler" or "RK4"

std::string	dirout_
	output directory if one is being used by a solver

bool	quiet_
	whether stuff should be printed during a solve

bool	silent_snap_
	whether to skip writing the solution vector to file when snapping but still execute after_snap()

unsigned long	neq_
	number of equations in the system of ODEs

double	t_
	time, initialized to zero

double	dt_
	time step is stored and updated during solves

double *	sol_
	array for the solution, changing over time

long unsigned	nstep_
	number of time steps

long unsigned	neval_
	function evaluation counter, must be incremented in step() when defined

long unsigned	icheck_
	interval of steps after which to check for nans and infs (zero to ignore)

double **	Jac_
	storage for the ODE system's Jacobian matrix, only allocated for the methods that need it

long unsigned	nJac_
	counter for jacobian evaluations

double	absjacdel_
	absolute adjustment fraction for numerical Jacobian, if needed

double	reljacdel_
	relative adjustment fraction for numerical Jacobian, if needed

Detailed Description

Explicit 5/4 pair, also with 3rd, 2nd, and 1st order embedded methods, from Cash & Karp.

This class implements a 5th order method developed by Cash and Karp (reference below) which includes embeddes solutions of order 1, 2, 3, and 4. It's a complete family of solutions up to order 5. The lower order solutions can be used to vary the solution's order and control the step size in sophisticated ways, canceling a step early if the error estimate is large. The fact that function evaluations are made fairly evenly through the interval of a time step is also advantageous for surveying potential trouble and controlling the step.

So far, the sophisticated time stepping is not implemented, so this solver simply uses the 4th and 5th order solutions for adaptation.

+ J. R. Cash, A. H. Karp. "A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides", ACM Transactions on Mathematical Software 16: 201-222, 1990. doi:10.1145/79505.79507
+ https://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method

Definition at line 21 of file ode_rkck.h.

Constructor & Destructor Documentation

◆ OdeRKCK()

ode::OdeRKCK::OdeRKCK ( unsigned long neq )

constructs

Parameters

[in] neq size of ODE sytem

Definition at line 7 of file ode_rkck.cc.

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

include/ode/ode_rkck.h
src/ode_rkck.cc

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ OdeRKCK()