num_prob_collect::ode::kaps_problem Class Reference

Class of Kaps' problem [15]. More...

#include <num_prob_collect/ode/kaps_problem.h>

Collaboration diagram for num_prob_collect::ode::kaps_problem:

Public Types
using	jacobian_type = Eigen::Matrix2d
	Type of Jacobian.
using	scalar_type = double
	Type of scalars.
using	variable_type = Eigen::Vector2d
	Type of variables.

Public Member Functions
	kaps_problem (double epsilon)
	Constructor.
auto	diff_coeff () const noexcept -> const variable_type &
	Get the differential coefficient.
void	evaluate_on (double, const variable_type &variable, num_collect::ode::evaluation_type evaluations)
	Evaluate on a (time, variable) pair.
auto	jacobian () const noexcept -> const jacobian_type &
	Get the Jacobian.

Static Public Attributes
static constexpr auto	allowed_evaluations
	Allowed evaluations.

Private Attributes
variable_type	diff_coeff_ {}
	Differential coefficient.
double	epsilon_
	Parameter.
jacobian_type	jacobian_ {}
	Jacobian.

Detailed Description

Class of Kaps' problem [15].

This ODE is as following:

\begin{aligned} \dot{y_1} & = -(\varepsilon^{-1} + 2) y_1 + \varepsilon^{-1} y_2^2 \\ \dot{y_2} &= y_1 - y_2 - y_2^2 \end{aligned}

For \( 0 \le t \le 1 \), exact solution is as following (for all \(\varepsilon\)):

\begin{aligned} y_1 &= \exp(-2t) \\ y_2 &= \exp(-t) \\ \end{aligned}

This problem is stiff for small \(\varepsilon\).

Definition at line 47 of file kaps_problem.h.

Member Typedef Documentation

jacobian_type

using num_prob_collect::ode::kaps_problem::jacobian_type = Eigen::Matrix2d

Type of Jacobian.

Definition at line 56 of file kaps_problem.h.

scalar_type

using num_prob_collect::ode::kaps_problem::scalar_type = double

Type of scalars.

Definition at line 53 of file kaps_problem.h.

variable_type

using num_prob_collect::ode::kaps_problem::variable_type = Eigen::Vector2d

Type of variables.

Definition at line 50 of file kaps_problem.h.

Constructor & Destructor Documentation

kaps_problem()

num_prob_collect::ode::kaps_problem::kaps_problem ( double epsilon )

inlineexplicit

Constructor.

Parameters

[in]

epsilon

Parameter in the equation.

Definition at line 67 of file kaps_problem.h.

Member Function Documentation

diff_coeff()

auto num_prob_collect::ode::kaps_problem::diff_coeff ( ) const -> const variable_type&

inlinenodiscardnoexcept

Get the differential coefficient.

Returns

Differential coefficient.

Definition at line 95 of file kaps_problem.h.

evaluate_on()

void num_prob_collect::ode::kaps_problem::evaluate_on ( double , const variable_type & variable, num_collect::ode::evaluation_type evaluations )

inline

Evaluate on a (time, variable) pair.

Parameters

[in]	variable	Variable.
[in]	evaluations	Evaluation types.

Definition at line 75 of file kaps_problem.h.

jacobian()

auto num_prob_collect::ode::kaps_problem::jacobian ( ) const -> const jacobian_type&

inlinenodiscardnoexcept

Get the Jacobian.

Returns

Jacobian.

Definition at line 104 of file kaps_problem.h.

Member Data Documentation

allowed_evaluations

auto num_prob_collect::ode::kaps_problem::allowed_evaluations

staticconstexpr

Initial value:

=
        num_collect::ode::evaluation_type{.diff_coeff = true, .jacobian = true}

Allowed evaluations.

Definition at line 59 of file kaps_problem.h.

diff_coeff_

variable_type num_prob_collect::ode::kaps_problem::diff_coeff_ {}

private

Differential coefficient.

Definition at line 113 of file kaps_problem.h.

epsilon_

double num_prob_collect::ode::kaps_problem::epsilon_

private

Parameter.

Definition at line 110 of file kaps_problem.h.

jacobian_

jacobian_type num_prob_collect::ode::kaps_problem::jacobian_ {}

private

Jacobian.

Definition at line 116 of file kaps_problem.h.

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

• problems/include/num_prob_collect/ode/kaps_problem.h