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nortonDP.f90
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program norton
use, intrinsic :: iso_fortran_env, only: qp=>real128
implicit none
!valores iniciales
real(qp), parameter :: x10 = 30.0_qp
real(qp), parameter :: x20 = 0.0_qp
real(qp), parameter :: g = 0.1_qp
real(qp), parameter :: d = 0.04_qp
real(qp), parameter :: a = 0.1_qp
real(qp), parameter :: x_max = 40.0_qp
real(qp), parameter :: t0 = 0.0_qp
real(qp), parameter :: t_max = 100.0_qp
!parametros iniciales
real(qp), parameter :: tinny = 0.0e-30_qp
integer , parameter :: max_steps = 10000
integer , parameter :: N_equ = 2 ! Numero de ecuaciones
integer :: step = 0
real(qp) :: dt = 0.05_qp
real(qp) :: dt_next = 0.0_qp
real(qp) :: t, farmaco, x1, x2
real(qp) :: r(N_equ), tmp(N_equ)
!**********************************************************************
t = t0 ! valores iniciales
r = [ x10, x20 ]
open(1,file='norton.dat') ! llenando archivo
!**********************************************************************
do ! resolviendo
write(1,*) t, r(1)+r(2), r(1), r(2), farmaco
print*, t, r(1)+r(2), r(1), r(2), farmaco
if( t .ge. t_max .or. step .ge. max_steps ) exit
step = step + 1
if ((t + dt) .gt. t_max) dt = t_max-t
call adaptativo(r,t,dt,dt_next,tmp)
t = t + dt
r = r + tmp
dt=min(dt_next,0.25_qp)
farmaco = 30.0_qp*(sqrt(t)/(sqrt(10.0_qp)+sqrt(t)))
x1 = r(1)
x2 = r(2)
end do
close(1)
print*,'terminadon en ',step,'pasos.'
call system('gnuplot -c norton.gplot')
!**********************************************************************
contains
!**********************************************************************
pure function f(r, t) ! Aqui se colocan las ecuaciones a resol
real(qp), intent(in) :: r(N_equ) ! Valores
real(qp), intent(in) :: t ! Tiempo
real(qp) :: far ! Farmaco
real(qp) :: f(N_equ)
real(qp) :: u,v
far = 30.0_qp*(sqrt(t)/(sqrt(10.0_qp)+sqrt(t)))
u = r(1)
v = r(2)
if( u .ne. 0.0_qp ) then
f(1) = g*u*log(x_max/u)-a*far*u
else
f(1) = 0.0_qp
endif
f(2) = a*far*u-d*v
end function f
!**********************************************************************
subroutine dopri(r, t, dt, errores, ytemp)
real(qp), intent(in) :: r(N_equ) ! Valores
real(qp), intent(in) :: t ! Paso
real(qp), intent(in) :: dt ! Tamano de paso
real(qp), intent(out) :: errores(N_equ),ytemp(N_equ)
real(qp) :: k1(N_equ),k2(N_equ),k3(N_equ),k4(N_equ)
real(qp) :: k5(N_equ),k6(N_equ),k7(N_equ)
! parametros de tiempo
real(qp),parameter :: a2 = 1.0_qp / 5.0_qp
real(qp),parameter :: a3 = 3.0_qp / 10.0_qp
real(qp),parameter :: a4 = 4.0_qp / 5.0_qp
real(qp),parameter :: a5 = 8.0_qp / 9.0_qp
! parametros de paso intermedio
real(qp),parameter :: b21 = 1.0_qp / 5.0_qp
real(qp),parameter :: b31 = 3.0_qp / 40.0_qp
real(qp),parameter :: b32 = 9.0_qp / 40.0_qp
real(qp),parameter :: b41 = 44.0_qp / 45.0_qp
real(qp),parameter :: b42 = -56.0_qp / 15.0_qp
real(qp),parameter :: b43 = 32.0_qp / 9.0_qp
real(qp),parameter :: b51 = 19372.0_qp / 6561.0_qp
real(qp),parameter :: b52 = -25360.0_qp / 2187.0_qp
real(qp),parameter :: b53 = 64448.0_qp / 6561.0_qp
real(qp),parameter :: b54 = -212.0_qp / 729.0_qp
real(qp),parameter :: b61 = 9017.0_qp / 3168.0_qp
real(qp),parameter :: b62 = -355.0_qp / 33.0_qp
real(qp),parameter :: b63 = 46732.0_qp / 5247.0_qp
real(qp),parameter :: b64 = 49.0_qp / 176.0_qp
real(qp),parameter :: b65 = -5103.0_qp / 18656.0_qp
real(qp),parameter :: b71 = 35.0_qp / 384.0_qp
real(qp),parameter :: b73 = 500.0_qp / 1113.0_qp
real(qp),parameter :: b74 = 125.0_qp / 192.0_qp
real(qp),parameter :: b75 = -2187.0_qp / 6784.0_qp
real(qp),parameter :: b76 = 11.0_qp / 84.0_qp
! parametros rk5
real(qp),parameter :: d1 = 5179.0_qp / 57600.0_qp
real(qp),parameter :: d3 = 7571.0_qp / 16695.0_qp
real(qp),parameter :: d4 = 393.0_qp / 640.0_qp
real(qp),parameter :: d5 = -92097.0_qp / 339200.0_qp
real(qp),parameter :: d6 = 187.0_qp / 2100.0_qp
real(qp),parameter :: d7 = 1.0_qp / 40.0_qp
! parametros error
real(qp),parameter :: e1 = 71.0_qp/57600.0_qp !c1 - d1
real(qp),parameter :: e3 =-71.0_qp/16695.0_qp !c3 - d3
real(qp),parameter :: e4 = 71.0_qp/1920.0_qp !c4 - d4
real(qp),parameter :: e5 =-17253.0_qp/339200.0_qp !c5 - d5
real(qp),parameter :: e6 = 22.0_qp/525.0_qp !c6 - d6
real(qp),parameter :: e7 =-1.0_qp/40.0_qp ! - d7
k1 = dt*f(r ,t )
k2 = dt*f(r + ( b21*k1 ),t + a2*dt)
k3 = dt*f(r + ( b31*k1 + b32*k2 ),t + a3*dt)
k4 = dt*f(r + ( b41*k1 + b42*k2 + b43*k3 ),t + a4*dt)
k5 = dt*f(r + ( b51*k1 + b52*k2 + b53*k3 + b54*k4 ),t + a5*dt)
k6 = dt*f(r + ( b61*k1 + b62*k2 + b63*k3 + b64*k4 + b65*k5 ),t + dt)
k7 = dt*f(r + ( b71*k1 + b73*k3 + b74*k4 + b75*k5 + b76*k6 ),t + dt)
ytemp = ( d1*k1 + d3*k3 + d4*k4 + d5*k5 + d6*k6 +d7*k7) !rk5
errores = dt*abs( e1*k1 + e3*k3 + e4*k4 + e5*k5 + e6*k6 + e7*k7 ) ! rk5-rk4
end subroutine dopri
!**********************************************************************
subroutine adaptativo(r,t,dt,dt_next,tmp)
real(qp), intent(in) :: r(N_equ) ! Valores
real(qp), intent(in) :: t ! Paso
real(qp), intent(inout) :: dt ! Tamano de paso
real(qp), intent(out) :: dt_next
real(qp), intent(out) :: tmp(N_equ)
real(qp), parameter :: safety = 0.9_qp
real(qp), parameter :: e_con = 1.89e-4_qp
real(qp), parameter :: eps = 1.0e-9_qp
real(qp), parameter :: PGROW = -0.2_qp
real(qp), parameter :: PSHRNK = -0.25_qp
real(qp) :: errores(N_equ), ytemp(N_equ), yscal(N_equ)
real(qp) :: dt_temp, t_new, e_max
do
call dopri(r,t,dt,errores,ytemp)
yscal = r+dt*f(r, t)+tinny
e_max = maxval(abs(errores/yscal))/eps
if ( e_max .gt. 1.0_qp ) then
dt_temp=safety*dt*(e_max**PSHRNK)
dt=sign(max(abs(dt_temp),0.1_qp*abs(dt)),dt)
t_new=t+dt
if (t_new .eq. t) then
PRINT*,'Paso demasiado pequeño en t=', t
stop
endif
else
tmp=ytemp
exit
endif
enddo
if (e_max .gt. e_con) then
dt_next=safety*dt*(e_max**PGROW)
else
dt_next=2.0_qp*dt
endif
end subroutine adaptativo
!**********************************************************************
end program norton