mm::AdamsBashforth< Scalar, num_steps > Class Template Reference

#include <AdamsBashforth_fwd.hpp>

Detailed Description

template<typename Scalar, int num_steps>
class mm::AdamsBashforth< Scalar, num_steps >

Class representing an AdamsBashforth method, an explicit linear multistep method.

Template Parameters

Scalar	Type of scalars to use for calculations, e.g. double.
num_steps	Number of previous steps the method uses.

Usage example:

    /*
     * Solving:
     * x' = -y
     * y' = x
     *
     * with solution (x, y) = (cos(t), sin(t))
     */
 
    std::function<Eigen::VectorXd(double, const Eigen::VectorXd&)> func =
            [](double, const Eigen::VectorXd& y) {
                Eigen::VectorXd r(2);
                r(0) = -y(1);
                r(1) = y(0);
                return r;
            };
 
    double tmax = 2*PI;
    double dt = 0.1;
    Eigen::VectorXd y0(2); y0 << 1.0, 0.0;
    auto solver = integrators::ExplicitMultistep::AB3().solve(func, 0.0, tmax, dt, y0);
    std::cout << solver << std::endl;
    for (auto step : solver) {
        std::cout << step << std::endl;
        if (step.is_last()) {
            std::cout << "This is the last step." << std::endl;
        }
        // Read/write access to current time and value.
        step.time();
        step.value();
    }

Definition at line 29 of file AdamsBashforth_fwd.hpp.

Public Member Functions
	AdamsBashforth (const Eigen::Matrix< scalar_t, steps, 1 > &b)
	Construct an num_steps-step Adams Bashforth method with coefficients b, given as \(y_{n+s} = y_{n+s-1} + h \sum_{j=0}^{s-1} b_j f(t_j, y_j)\). More...
template<typename func_t >
Integrator< func_t >	solve (const func_t &func, scalar_t t0, scalar_t t_max, scalar_t dt, const Eigen::VectorXd &y0) const
	Returns a solver using this method. More...
template<typename initial_method_t , typename func_t >
Integrator< func_t, initial_method_t >	solve (const initial_method_t &method, const func_t &func, scalar_t t0, scalar_t t_max, scalar_t dt, const Eigen::VectorXd &y0) const
	Same as AdamsBashforth::solve, but offers the option of supplying your own initial method. More...

Public Types
enum	{ steps = num_steps }
typedef Scalar	scalar_t
	floating point type More...

Classes
class	Integrator
	Integrator class for AB methods. More...

Friends
template<typename scalar_t , int stages>
std::ostream &	operator<< (std::ostream &os, const AdamsBashforth< scalar_t, stages > &)
	Output the method's tableau for debugging. More...

Private Member Functions
template<typename func_t >
Eigen::VectorXd	step (const func_t &func, scalar_t t, const Eigen::Matrix< scalar_t, Eigen::Dynamic, steps > &last_ys, scalar_t dt) const
	Returns next value. More...

Private Attributes
Eigen::Matrix< scalar_t, steps, 1 >	b_
	coefficients of the multistep method More...

Member Enumeration Documentation

anonymous enum

template<typename Scalar , int num_steps>

anonymous enum

Enumerator
steps	number of steps of the multistep method

Definition at line 32 of file AdamsBashforth_fwd.hpp.

Constructor & Destructor Documentation

AdamsBashforth()

template<typename Scalar , int num_steps>

mm::AdamsBashforth< Scalar, num_steps >::AdamsBashforth ( const Eigen::Matrix< scalar_t, steps, 1 > &  b )

inline

Construct an num_steps-step Adams Bashforth method with coefficients b, given as \(y_{n+s} = y_{n+s-1} + h \sum_{j=0}^{s-1} b_j f(t_j, y_j)\).

Parameters

b	Vector of size num_steps representing the coefficients of the method.

Definition at line 44 of file AdamsBashforth_fwd.hpp.

Member Function Documentation

solve() [1/2]

template<typename Scalar , int num_steps>

template<typename func_t >

Integrator<func_t> mm::AdamsBashforth< Scalar, num_steps >::solve ( const func_t &  func, scalar_t  t0, scalar_t  t_max, scalar_t  dt, const Eigen::VectorXd &  y0  ) const

inline

Returns a solver using this method.

Parameters

func	Function to integrate.
t0	Start time.
t_max	End time.
dt	Time step.
y0	Initial value.

Warning

Last step might not finish exactly on t_max. The number of steps is calculated as std::ceil((t_max - t0)/dt).

Returns

A solver object.

Definition at line 203 of file AdamsBashforth_fwd.hpp.

solve() [2/2]

template<typename Scalar , int num_steps>

template<typename initial_method_t , typename func_t >

Integrator<func_t, initial_method_t> mm::AdamsBashforth< Scalar, num_steps >::solve ( const initial_method_t &  method, const func_t &  func, scalar_t  t0, scalar_t  t_max, scalar_t  dt, const Eigen::VectorXd &  y0  ) const

inline

Same as AdamsBashforth::solve, but offers the option of supplying your own initial method.

Definition at line 211 of file AdamsBashforth_fwd.hpp.

step()

template<typename Scalar , int num_steps>

template<typename func_t >

Eigen::VectorXd mm::AdamsBashforth< Scalar, num_steps >::step ( const func_t &  func, scalar_t  t, const Eigen::Matrix< scalar_t, Eigen::Dynamic, steps > &  last_ys, scalar_t  dt  ) const

inlineprivate

Returns next value.

Definition at line 220 of file AdamsBashforth_fwd.hpp.

Friends And Related Function Documentation

operator<<

template<typename Scalar , int num_steps>

template<typename scalar_t , int stages>

std::ostream& operator<< ( std::ostream &  os, const AdamsBashforth< scalar_t, stages > &    )

friend

Output the method's tableau for debugging.

Member Data Documentation

b_

template<typename Scalar , int num_steps>

Eigen::Matrix<scalar_t, steps, 1> mm::AdamsBashforth< Scalar, num_steps >::b_

private

coefficients of the multistep method

Definition at line 36 of file AdamsBashforth_fwd.hpp.

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

• include/medusa/bits/integrators/AdamsBashforth_fwd.hpp