Classes
class	NewtonBackwardEuler
	Nonlinear system solver for OdeBackwardEuler. More...

class	NewtonGauss6
	Nonlinear system solver for OdeGauss6. More...

class	NewtonGeng5
	Nonlinear system solver for OdeGeng5. More...

class	NewtonLobattoIIIC6
	Nonlinear system solver for OdeLobattoIIIC6. More...

class	NewtonRadauIIA5
	Nonlinear system solver for OdeRadauIIA5. More...

class	NewtonSDIRK43
	Nonlinear system solver for OdeSDIRK43. More...

class	OdeAdaptive
	Base class implementing solver functions with adaptive time steps. More...

class	OdeBackwardEuler
	Backward Euler's method, unconditionally stable but relatively inaccurate. More...

class	OdeBase
	Lowest base class for all solvers. More...

class	OdeDoPri54
	Popular explicit 5/4 pair from Dormand & Prince. More...

class	OdeDoPri87
	Explicit 8/7 pair from Dormand & Prince. More...

class	OdeEmbedded
	Base clase implementing methods for embedded Runge-Kutta error estimation. More...

class	OdeERK
	Base class providing space for temporary solutions moving through RK stages. More...

class	OdeEuler
	The simplest runge kutta method, forward Euler's. More...

class	OdeGauss6
	The sixth-order, A-stable, fully-implicit Gauss-Legendre method with 3 stages. More...

class	OdeGeng5
	The fifth-order, symplectic, fully-implicit Geng integrator with 3 stages. More...

class	OdeGRK4A
	Fourth-order, A-stable, adaptive Rosenbrock method from Kaps and Rentrop. More...

class	OdeIRK
	Provides a large vector containing the slope values of all stages with pointers to each of the individual stages. More...

class	OdeLobattoIIIC6
	The sixth-order, L-stable, fully-implicit Lobatto IIIC method with 4 stages. More...

class	OdeNewton
	Newton's method for nonlinear systems of equations. More...

class	OdeNewtonBridge
	Templated base class connecting solver objects and OdeNewton objects. More...

class	OdeNewtonIRK
	Extension of OdeNewtonBridge class for fully implicit methods. More...

class	OdeNewtonSDIRK
	Extension of OdeNewtonBridge class for fully SDIRK methods. More...

class	OdeRadauIIA5
	The fifth-order, L-stable, fully-implicit Radau IIA method with 3 stages. More...

class	OdeRK
	Provides space for stage slope values, an array of arrays for k values. More...

class	OdeRK4
	The classic Runge-Kutta 4th order method. More...

class	OdeRK43
	This class implements a 3rd and 4th order method with the FSAL (first same as last) property. More...

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

class	OdeRKF32
	2nd and 3rd order solver developed by Fehlberg More...

class	OdeRosenbrock
	Base class for Rosenbrock methods. More...

class	OdeROW6A
	6th order, A-stable Rosenbrock method More...

class	OdeSDIRK43
	L-stable 4/3 SDIRK pair. More...

class	OdeSsp3
	Strong stability preserving method of order 3. More...

class	OdeTrapz
	Second order, explicit trapezoidal rule. More...

class	OdeVern65
	Jim Verner's "most efficient" 6/5 pair. More...

class	OdeVern76
	Jim Verner's "most efficient" 7/6 pair. More...

class	OdeVern98
	Jim Verner's "most efficient" 9/8 pair. More...

Functions
void	ode_check_write (const char *fn)
	check if a file can be written (opened in write mode)

void	ode_print_exit (const char *msg)
	print a message and exit with failure

std::string	ode_int_to_string (long i)
	converts an integer into a string

void	ode_crout_forw_sub (double *L, double b, int p, int n, double out)
	Crout forward substitution.

void	ode_back_sub (double *U, double b, int n, double *out)
	Backward substitution.

void	ode_crout_LU (double *A, int n, int p)
	Crout LU decomposition.

void	ode_solve_LU (double *LU, int p, double b, int n, double out)
	Solves a matrix equation where the matrix has already be crout LU decomposed.

void	ode_solve_A (double *A, double b, int n, double *out)
	Solves a matrix equation A x = b with crout LU decomposition.

void	ode_solve_tridiag (double *T, double r, double temp, int n, double out)
	Solves a tridiagonal matrix equation.

double	ode_max2 (double a, double b)
	Simple maximum of two doubles.

double	ode_min2 (double a, double b)
	Simple minimum of two doubles.

bool	ode_is_close (double a, double b, double thresh)
	Checks if two numbers are very close to each other.

template<class T >
void	ode_write (char const fn, T a, unsigned long n)
	write an array to a binary file

Detailed Description

These classes provides some variables of convenience when connecting the Newton base (which is left as a generic Newton solver for potential reuse elsewhere) and the systems required for implicit methods.

Function Documentation

◆ ode_back_sub()

void ode::ode_back_sub	(	double **	U,
		double *	b,
		int	n,
		double *	out )

Backward substitution.

Performs backward substitution to solve an upper triangular matrix equation input:

Parameters

[in]	U	n by n upper triangular matrix
[in]	b	right hand side of matrix equation U*out = b
[in]	n	dimensions of A and length of b
[out]	out	array of length n, result of substitution

Definition at line 18 of file ode_linalg.cc.

◆ ode_check_write()

void ode::ode_check_write ( const char * fn )

check if a file can be written (opened in write mode)

Parameters

[in] fn desired file name

Definition at line 7 of file ode_io.cc.

◆ ode_crout_forw_sub()

void ode::ode_crout_forw_sub	(	double **	L,
		double *	b,
		int *	p,
		int	n,
		double *	out )

Crout forward substitution.

Performs forward substitution to solve a lower triangular matrix equation where the elements on the main diagonal of the lower triangular matrix are assumed to all be 1.

Parameters

[in]	L	n by n lower triangular matrix
[in]	b	right hand side of matrix equation U*out = b
[in]	p	array of permutation indices from crout_LU
[in]	n	dimensions of A and length of b
[out]	out	array of length n, result of substitution

Definition at line 7 of file ode_linalg.cc.

◆ ode_crout_LU()

void ode::ode_crout_LU	(	double **	A,
		int	n,
		int *	p )

Crout LU decomposition.

performs LU decomposition with partial pivoting on the matrix A and sets permutation indices in the array p, following the outline in the book:

Demmel, James W. Applied numerical linear algebra. Vol. 56. Siam, 1997.
Parameters

A matrix of size n to decompose (overwritten)

[in] n size of square matrix

[out] p integer array loaded with permutation indices

Definition at line 29 of file ode_linalg.cc.

◆ ode_int_to_string()

std::string ode::ode_int_to_string ( long i )

converts an integer into a string

Definition at line 25 of file ode_io.cc.

◆ ode_is_close()

bool ode::ode_is_close	(	double	a,
		double	b,
		double	thresh )

Checks if two numbers are very close to each other.

Definition at line 17 of file ode_util.cc.

◆ ode_max2()

double ode::ode_max2	(	double	a,
		double	b )

Simple maximum of two doubles.

Definition at line 7 of file ode_util.cc.

◆ ode_min2()

double ode::ode_min2	(	double	a,
		double	b )

Simple minimum of two doubles.

Definition at line 12 of file ode_util.cc.

◆ ode_print_exit()

void ode::ode_print_exit ( const char * msg )

print a message and exit with failure

Parameters

[in] msg the message to print before exiting the program

Definition at line 17 of file ode_io.cc.

◆ ode_solve_A()

void ode::ode_solve_A	(	double **	A,
		double *	b,
		int	n,
		double *	out )

Solves a matrix equation A x = b with crout LU decomposition.

Parameters

[in]	A	matrix, is overwritten
[in]	b	right-hand side of matrix equation
[in]	n	size of matrix and arrays
[out]	out	solution to linear system

Definition at line 84 of file ode_linalg.cc.

◆ ode_solve_LU()

void ode::ode_solve_LU	(	double **	LU,
		int *	p,
		double *	b,
		int	n,
		double *	out )

Solves a matrix equation where the matrix has already be crout LU decomposed.

Parameters

[in]	LU	crout LU decomposed matrix
[in]	p	permutation indices
[in]	b	right-hand side of matrix equation
[in]	n	size of matrix and arrays
[out]	out	solution to linear system

Definition at line 76 of file ode_linalg.cc.

◆ ode_solve_tridiag()

void ode::ode_solve_tridiag	(	double **	T,
		double *	r,
		double *	temp,
		int	n,
		double *	out )

Solves a tridiagonal matrix equation.

The input matrix T must be in banded storage. This means that the diagonals are placed on rows so that the trigiagonal matrix A

A = | a00  a01   0    0  |
    | a10  a11  a12   0  |
    |  0   a21  a22  a23 |
    |  0    0   a32  a33 |

is stored in banded form as the array T

T = |  *   a01  a12  a23 |
    | a00  a11  a22  a33 |
    | a10  a21  a31   *  |

and the value of the asterisk elements doesn't matter.

Parameters

[in]	T	tridiagonal matrix in banded storage form
[in]	r	right-hand side of matrix equation
[in]	temp	temporary array
[in]	n	size of matrix and arrays
[out]	out	solution to linear system

Definition at line 98 of file ode_linalg.cc.

◆ ode_write()

template<class T >

void ode::ode_write	(	char const *	fn,
		T *	a,
		unsigned long	n )

write an array to a binary file

Parameters

[in]	fn	file name or path
[in]	a	array of values to write
[in]	n	size of array or number of elements to write

Definition at line 27 of file ode_io.h.

	A	matrix of size n to decompose (overwritten)
[in]	n	size of square matrix
[out]	p	integer array loaded with permutation indices

Classes

Functions

Detailed Description

Function Documentation

◆ ode_back_sub()

◆ ode_check_write()

◆ ode_crout_forw_sub()

◆ ode_crout_LU()

◆ ode_int_to_string()

◆ ode_is_close()

◆ ode_max2()

◆ ode_min2()

◆ ode_print_exit()

◆ ode_solve_A()

◆ ode_solve_LU()

◆ ode_solve_tridiag()

◆ ode_write()