Explicit extrapolation scheme for time integration. More...

Inheritance diagram for ext_time_scheme::ext_time_scheme_t:

Collaboration diagram for ext_time_scheme::ext_time_scheme_t:

Static Public Member Functions
procedure, nopass	compute_coeffs (coeffs, dt, order)
	Compute the scheme coefficients.

procedure, nopass	compute_modified_coeffs (coeffs, dt)
	Compute the coefficients for the modified EXT scheme.

Detailed Description

Compute the value at the current time-step by evaluating a polynomial built using the values on previous time-steps.

For a constant time-step corresponds to the following schemes of order 1 to 3:

Order 1: \( u^{n+1} = u^n \)
Order 2: \( u^{n+1} = 2u^n - u^{n-1} \), linear extrapolation
Order 3: \( u^{n+1} = 3u^n - 3u^{n-1} + u^{n-2} \) An additional scheme is available via compute_modified_coeffs, which is gives improved stability when combined with BDF2 in a advection-diffusion equation.
Order 3: \( u^{n+1} = 8/3u^n - 7/3u^{n-1} + 2/3u^{n-2} \)

Definition at line 84 of file ext_time_scheme.f90.

Member Function/Subroutine Documentation

procedure, nopass ext_time_scheme::ext_time_scheme_t::compute_coeffs	(	real(kind=rp), dimension(4), intent(out)	coeffs,
		real(kind=rp), dimension(10), intent(in)	dt,
		integer, intent(in)	order
	)

staticvirtual

Parameters

t	Timestep values, first element is the current timestep.
order	Order the scheme.

Definition at line 87 of file ext_time_scheme.f90.

procedure, nopass ext_time_scheme::ext_time_scheme_t::compute_modified_coeffs	(	real(kind=rp), dimension(4), intent(out)	coeffs,
		real(kind=rp), dimension(10), intent(in)	dt
	)

static

Parameters

t	Timestep values, first element is the current timestep.

Definition at line 89 of file ext_time_scheme.f90.

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