ode_nl_1s_mod Module Reference

ONE-STEP SOLVERS FOR NON LINEAR ODEs More...

Functions/Subroutines
logical function, public	check_ode_method_nl_1s (method)
	is 'method' a one-step non-linear ODE solver ? More...
subroutine, public	memsize_ode_nl_1s (n_Y, n_FY, method)
	required sizes to allocate memory More...
subroutine, public	set_solver_ode_nl_1s (slv, method)
	set the solver 'slv' to a predefined solver being given a method More...
subroutine, public	create_ode_nl_1s_sol (sol, pb, method)
	create memory for the ode_solution structure 'sol' More...
subroutine, public	solve_ode_nl_1s (sol, pb, t0, T, dt, method, out, check_overflow)
	solve with constant time-step More...
subroutine	nl_1s_fbe (sol, dt, t, pb)
	FORWARD/BacWard Euler. More...
subroutine	nl_1s_rk2 (sol, dt, t, pb)
	RK2. More...
elemental subroutine	phi_1 (z)
	phi_1 = ( exp(z) - 1 ) / z More...
elemental subroutine	phi_2 (z)
	phi_2 = (exp(z) - z - 1._RP)/z^2 More...
subroutine	nl_1s_fe (sol, dt, t, pb)
	Forward Euler. More...
subroutine	nl_1s_erk1 (sol, dt, t, pb)
	Exponential Euler. More...
subroutine	nl_1s_erk2_a (sol, dt, t, pb)
	Exponential RK2, type A ref = "Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems" Hochbruck, Ostermann, SIAM J. Numer. Anal. 2005 page 1082, tableau 1, c2 = 1/2. More...
subroutine	nl_1s_erk2_b (sol, dt, t, pb)
	Exponential RK2, type B ref = "Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems" Hochbruck, Ostermann, SIAM J. Numer. Anal. 2005 page 1082, tableau 2, c2 = 1/2. More...
subroutine	nl_1s_modif_erk2_b (sol, dt, t, pb)
	Modified ERK2_B. More...
subroutine	nl_1s_modif_erk2_a (sol, dt, t, pb)
	Modified ERK2_A. More...
subroutine	nl_1s_rk4 (sol, dt, t, pb)
	RK4. More...

Detailed Description

ONE-STEP SOLVERS FOR NON LINEAR ODEs

One step solvers for ODE_PB_NL, see ode_problem_mod detailed description.

Author

Charles Pierre

Function/Subroutine Documentation

check_ode_method_nl_1s()

logical function, public ode_nl_1s_mod::check_ode_method_nl_1s

(

integer, intent(in)

method

)

is 'method' a one-step non-linear ODE solver ?

Definition at line 36 of file ode_NL_1s_mod.f90.

create_ode_nl_1s_sol()

subroutine, public ode_nl_1s_mod::create_ode_nl_1s_sol	(	type(ode_solution), intent(inout)	sol,
		type(ode_problem), intent(in)	pb,
		integer, intent(in)	method
	)

create memory for the ode_solution structure 'sol'

Definition at line 114 of file ode_NL_1s_mod.f90.

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memsize_ode_nl_1s()

subroutine, public ode_nl_1s_mod::memsize_ode_nl_1s	(	integer, intent(out)	n_Y,
		integer, intent(out)	n_FY,
		integer, intent(in)	method
	)

required sizes to allocate memory

returns iY, iFY depending on the method

• n_Y = required size for Y
• n_FY = required size for AY, BY

Definition at line 60 of file ode_NL_1s_mod.f90.

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nl_1s_erk1()

subroutine ode_nl_1s_mod::nl_1s_erk1 ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Exponential Euler.

Definition at line 338 of file ode_NL_1s_mod.f90.

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nl_1s_erk2_a()

subroutine ode_nl_1s_mod::nl_1s_erk2_a ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Exponential RK2, type A ref = "Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems" Hochbruck, Ostermann, SIAM J. Numer. Anal. 2005 page 1082, tableau 1, c2 = 1/2.

Definition at line 380 of file ode_NL_1s_mod.f90.

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nl_1s_erk2_b()

subroutine ode_nl_1s_mod::nl_1s_erk2_b ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Exponential RK2, type B ref = "Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems" Hochbruck, Ostermann, SIAM J. Numer. Anal. 2005 page 1082, tableau 2, c2 = 1/2.

Definition at line 472 of file ode_NL_1s_mod.f90.

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nl_1s_fbe()

subroutine ode_nl_1s_mod::nl_1s_fbe ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

FORWARD/BacWard Euler.

(y1 - y)/dt = a(y)*y1 + b(y)

updates y := y1

Na=0 => explicit Euler

Definition at line 201 of file ode_NL_1s_mod.f90.

nl_1s_fe()

subroutine ode_nl_1s_mod::nl_1s_fe ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Forward Euler.

Definition at line 309 of file ode_NL_1s_mod.f90.

nl_1s_modif_erk2_a()

subroutine ode_nl_1s_mod::nl_1s_modif_erk2_a ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Modified ERK2_A.

Definition at line 607 of file ode_NL_1s_mod.f90.

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nl_1s_modif_erk2_b()

subroutine ode_nl_1s_mod::nl_1s_modif_erk2_b ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

Modified ERK2_B.

Definition at line 552 of file ode_NL_1s_mod.f90.

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nl_1s_rk2()

subroutine ode_nl_1s_mod::nl_1s_rk2 ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

RK2.

Definition at line 233 of file ode_NL_1s_mod.f90.

nl_1s_rk4()

subroutine ode_nl_1s_mod::nl_1s_rk4 ( type(ode_solution), intent(inout)  sol, real(rp), intent(in)  dt, real(rp), intent(in)  t, type(ode_problem), intent(in)  pb  )

private

RK4.

Definition at line 675 of file ode_NL_1s_mod.f90.

phi_1()

elemental subroutine ode_nl_1s_mod::phi_1 ( real(rp), intent(inout)  z )

private

phi_1 = ( exp(z) - 1 ) / z

Definition at line 275 of file ode_NL_1s_mod.f90.

phi_2()

elemental subroutine ode_nl_1s_mod::phi_2 ( real(rp), intent(inout)  z )

private

phi_2 = (exp(z) - z - 1._RP)/z^2

Definition at line 289 of file ode_NL_1s_mod.f90.

set_solver_ode_nl_1s()

subroutine, public ode_nl_1s_mod::set_solver_ode_nl_1s	(	procedure(ode_nl_1s_solver), pointer	slv,
		integer, intent(in)	method
	)

set the solver 'slv' to a predefined solver being given a method

Definition at line 82 of file ode_NL_1s_mod.f90.

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solve_ode_nl_1s()

subroutine, public ode_nl_1s_mod::solve_ode_nl_1s	(	type(ode_solution), intent(inout)	sol,
		type(ode_problem), intent(in)	pb,
		real(rp), intent(in)	t0,
		real(rp), intent(in)	T,
		real(rp), intent(in)	dt,
		integer, intent(in)	method,
		procedure(ode_output_proc)	out,
		logical, intent(in)	check_overflow
	)

solve with constant time-step

Definition at line 136 of file ode_NL_1s_mod.f90.

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