Euler Forward method

!Este Programa fue realizado por Lillieskold, Thomas Enrique
!Instituto Universitario Aeronautico - 2023
!Docentes: Giovacchini, Juan Pablo; Sacco, Carlos
!Asignatura: Calculo Numerico
!-------------------------------------------------------------------------------

!----------------DECLARACION DE VARIABLES PARA Euler-----------------------------
MODULE Data_Euler
REAL(8),PARAMETER::t_min=0.d0
REAL(8),PARAMETER:: t_max=2.d0
REAL(8),PARAMETER:: V_0=1.d0
REAL(8),PARAMETER:: k=0.1
INTEGER,PARAMETER:: dim=(t_max-t_min)/k
END MODULE Data_Euler


!--------------------------------------INICIO DEL MAIN PROGRAM-----------------------------------------------------------------------------
Program Euler_Forward
USE Data_Euler
Implicit none

REAL(8),DIMENSION(dim)::aprox_1
REAL(8),DIMENSION(2*dim)::aprox_2
REAL(8),DIMENSION(4*dim)::aprox_3


!CALL Euler(aprox_1,k,dim)
CALL Euler(aprox_2,k/2.d0,2*dim)
!CALL Euler(aprox_3,k/4.d0,4*dim)

CALL Error_Global(aprox_2,k/2.d0)

!CALL Cociente_con_exacta(aprox_1,aprox_2)

!CALL Cociente_sin_exacta(aprox_1,aprox_2,aprox_3)

END PROGRAM

!---------------------------------------FINAL DEL MAIN PROGRAM------------------------------------------------------------------------------



!---------------------------------------SUBRUTINA EULER-------------------------------------------------------------------------------------
SUBROUTINE Euler(aprox,Inc,ext)
USE Data_Euler
Implicit none
REAL(8) v_n,v_o,func,t_i,Inc
INTEGER ext
REAL(8),DIMENSION(ext)::aprox
Integer Iter,i

v_o=v_0
t_i=t_min
iter=0

    OPEN(3,FILE="Write_outs_k=0.1")
    PRINT*, "      Iter    T_i                      v_n"
    DO i=1,ext,1
        iter=iter+1
        aprox(i)=v_o
        v_n = v_o + Inc * func(v_o,t_i)
        Write(3,*) t_i,aprox(i)
        PRINT*, Iter,t_i,aprox(i)
        v_o=v_n
        t_i=t_i+Inc
    END DO
        PRINT*, "------------------------------------------------------------------------------------------------------"
END SUBROUTINE

REAL(8) FUNCTION func(y,x)
Implicit none
REAL(8) y,x
    func=-1.d0*y+ sin(2.d0*dacos(-1.d0)*x)  !Esta funcion es la que acompaña a la ecuacion diferencial
END FUNCTION



!---------------------------------------------SUBRUTINA ERROR GLOBAL----------------------------------------------------------
SUBROUTINE Error_Global(aprox_1,Inc)
USE Data_Euler
IMPLICIT NONE
REAL(8) t_i, exact_sol, Error_Glob,Inc
REAL(8),DIMENSION(2*dim)::aprox_1
INTEGER i
Error_Glob=0.d0

    t_i=t_min
    OPEN(4,file="Error_Global_k=0.1")
    PRINT*, "Error_Gobal_k=0.001"
    PRINT*, "         Iter  t_i                     Error_Glob"
    DO i=1,2*dim,1
        Error_Glob=abs(aprox_1(i)-exact_sol(t_i))
            WRITE(4,*) t_i,Error_Glob
            Print*, i,t_i, Error_Glob
        t_i=t_i+Inc
    END DO
    PRINT*, "-------------------------------------------------------------------------------------------------"
END SUBROUTINE



REAL(8) FUNCTION exact_sol(t_i)
Implicit none
REAL(8) t_i, A, denom

denom= 1.d0 + 4.d0 * dacos(-1.d0)**2.d0

A= 1.d0 + (2.d0 *  dacos(-1.d0))/ Denom

exact_sol= (1.d0/denom)* (sin(2.d0*dacos(-1.d0)*t_i) - (2.d0*dacos(-1.d0)*cos(2.d0*dacos(-1.d0)*t_i))) + A* exp(-t_i)

END FUNCTION


!------------------------------------------SUBRUTINA COCIENTE DE PRECISION CON SOLUCION EXACTA--------------------------------------------
SUBROUTINE Cociente_con_exacta(aprox_1,aprox_2)
USE Data_Euler
IMPLICIT NONE
REAL(8) Q,t_i,exact_sol
REAL(8),DIMENSION(dim)::aprox_1
REAL(8),DIMENSION(2*dim)::aprox_2
INTEGER i
t_i=t_min
    OPEN(10,FILE="cociente_con_exacta")
    DO i=1,dim,1
        Q=(aprox_1(i)-exact_sol(t_i))/(aprox_2(2*i-1)-exact_sol(t_i))
        WRITE(10,*) t_i,Q
        t_i=t_i+k
    END DO
END SUBROUTINE


!-----------------------------------------SUBRUTINA COCIENTE DE PRECISION SIN SOLUCION EXACTA---------------------------------------------
SUBROUTINE Cociente_sin_exacta(aprox_1,aprox_2,aprox_3)
USE Data_Euler
IMPLICIT NONE
REAL(8) Q,t_i
REAL(8),DIMENSION(dim)::aprox_1
REAL(8),DIMENSION(2*dim)::aprox_2
REAL(8),DIMENSION(4*dim)::aprox_3
INTEGER i
t_i=t_min
    OPEN(11,FILE="cociente_sin_exacta")
    DO i=1,dim,1
        Q=(aprox_1(i)-aprox_2(2*i-1))/(aprox_2(2*i-1)-aprox_3(4*i-3))
        WRITE(11,*) t_i,Q
        t_i=t_i+k
    END DO
END SUBROUTINE