Description

Implements split operators for linear pendulum.

Solve linear pendulum problem: \( \frac{dx}{dt} = v \), \( \frac{dv}{dt} = - \omega^2 x \). The exact solution is

\[ x(t)= x(0)\cos (\omega t) + \frac{v(0)}{\omega}\sin (\omega t), ~~~ v(t)= -x(0)\omega\sin (\omega t) + v(0)\cos (\omega t) \]

Derived types and interfaces
type	linear_pendulum_operators
	Simple operator splitting type for linear pendulum Extends operator splitting. More...

Functions/Subroutines
subroutine	push_x (this, dt)
	Implements the first operator of splitting for linear pendulum. More...

subroutine	push_v (this, dt)
	Implements the second operator of splitting for linear pendulum. More...

subroutine, public	sll_s_check_order (method, steps_fine, expected_order, test_passed)
	checks the order of a splitting method on the linear pendulum. used for unit testing. More...

Variables
real(kind=f64), parameter	omega = 2.0_f64
	frequency More...

real(kind=f64), parameter	x0 = 1.0_f64
	initial x for order checking More...

real(kind=f64), parameter	v0 = 2.0_f64
	initial v for order checking More...

real(kind=f64), parameter	t_final = 1.0_f64
	final time for order checking More...

Function/Subroutine Documentation

subroutine sll_m_linear_pendulum_operators::push_v	(	class(linear_pendulum_operators), intent(inout)	this,
		real(kind=f64), intent(in)	dt
	)

private

Implements the second operator of splitting for linear pendulum.

Parameters

[in,out]	this	object
[in]	dt	time step

subroutine sll_m_linear_pendulum_operators::push_x	(	class(linear_pendulum_operators), intent(inout)	this,
		real(kind=f64), intent(in)	dt
	)

private

Implements the first operator of splitting for linear pendulum.

Parameters

[in,out]	this	object
[in]	dt	time step

subroutine, public sll_m_linear_pendulum_operators::sll_s_check_order	(	integer(kind=i32), intent(in)	method,
		real(kind=f64), intent(in)	steps_fine,
		integer(kind=i32), intent(in)	expected_order,
		logical, intent(inout)	test_passed
	)

checks the order of a splitting method on the linear pendulum. used for unit testing.

Parameters

[in]	method	splitting method to be chosen from those implemented in sll_m_operator_splitting
[in]	steps_fine	number of steps on fine grid
[in]	expected_order	expected_order of the method
[in,out]	test_passed	check if test successful