Euler fortran (#411)

* Delete monte_carlo_pi.f90

* init

* further implementation

* next

* forward euler implementation

* revoked merge changed from bubble.f90

* Gitbook documentation

* fix fortran highlight

Author: depate

contents/forward_euler_method/code/fortran/euler.f90

@@ -0,0 +1,64 @@
+PROGRAM euler
+    
+    IMPLICIT NONE
+    LOGICAL                            :: is_approx
+    REAL(8), DIMENSION(:), ALLOCATABLE :: vec
+    REAL(8)                            :: time_step, threshold
+    INTEGER                            :: n
+
+    time_step = 0.01d0
+    n         = 100
+    threshold = 0.01d0
+    
+    ALLOCATE(vec(n))
+    CALL forward_euler(time_step, n, vec)
+    is_approx = check_result(vec, threshold, time_step)
+
+    WRITE(*,*) is_approx
+
+    DEALLOCATE(vec)
+    
+CONTAINS
+
+    SUBROUTINE forward_euler(time_step, n, vec)
+        
+        IMPLICIT NONE
+        REAL(8), DIMENSION(:), INTENT(OUT)   :: vec
+        REAL(8), INTENT(IN)                  :: time_step
+        INTEGER, INTENT(IN)                  :: n
+        INTEGER                              :: i
+
+        vec(1) = 1d0
+
+        DO i=1, n-1
+        
+            vec(i+1) = vec(i) - 3d0 * vec(i) * time_step
+
+        END DO
+    END SUBROUTINE
+
+    LOGICAL FUNCTION check_result(euler_result, threshold, time_step) 
+    
+        IMPLICIT NONE
+        REAL(8), DIMENSION(:), INTENT(IN) :: euler_result
+        REAL(8), INTENT(IN)               :: threshold, time_step 
+        REAL(8)                           :: time, solution
+        INTEGER                           :: i
+
+        check_result = .TRUE.
+
+        DO i = 1, SIZE(euler_result)
+
+            time = (i - 1) * time_step
+            solution = EXP(-3d0 * time)
+             
+            IF (ABS(euler_result(i) - solution) > threshold) THEN
+                
+                WRITE(*,*) euler_result(i), solution
+                check_result = .FALSE.
+
+            END IF
+        END DO
+    END FUNCTION
+END PROGRAM euler
+

contents/forward_euler_method/forward_euler_method.md

@@ -121,6 +121,8 @@ Full code for the visualization follows:
 [import, lang:"matlab"](code/matlab/euler.m)
 {% sample lang="swift" %}
 [import, lang:"swift"](code/swift/euler.swift)
+{% sample lang="f90" %}
+[import, lang:"fortran"](code/fortran/euler.f90)
 {% endmethod %}
 
 <script>