-
Notifications
You must be signed in to change notification settings - Fork 0
/
stepanovaDP.f90
166 lines (155 loc) · 6.72 KB
/
stepanovaDP.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
program stepanova
use, intrinsic :: iso_fortran_env, only: qp=>real128
implicit none
!valores iniciales
real(qp), parameter :: x0 = 1.0_qp
real(qp), parameter :: z0 = 0.0_qp
real(qp), parameter :: g = 0.6_qp
real(qp), parameter :: x_max = 7.5_qp
real(qp), parameter :: gama = 1.0_qp
real(qp), parameter :: kI = 0.5_qp
real(qp), parameter :: beta = 0.3_qp
real(qp), parameter :: delta = 0.4_qp
real(qp), parameter :: mu = 0.1_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, x1, x2
real(qp) :: r(N_equ), tmp(N_equ)
!**********************************************************************
t = t0 ! valores iniciales
r = [ x0, z0 ]
open(1,file='stepanova.dat') ! llenando archivo
!**********************************************************************
do ! resolviendo
write(1,*) t, r(1), r(2)
print*, t, r(1), r(2)
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,0.1_qp)
x1 = r(1)
x2 = r(2)
end do
print*,'terminadon en ',step,'pasos.'
close(1)
call system('gnuplot -c stepanova.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) :: f(N_equ)
real(qp) :: u,v
u = r(1)
v = r(2)
f(1) = g * u * (1.0_qp - u/x_max) - gama * u * v
f(2) = kI * ( u - beta * u**2 ) * v - delta * v + mu
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.e-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._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 stepanova