Initial data commit

Task/Euler-method/Fortran/euler-method.f

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+program euler_method
+use iso_fortran_env, only: real64
+implicit none
+
+abstract interface
+  ! a derivative dy/dt as function of y and t
+  function derivative(y, t)
+    use iso_fortran_env, only: real64
+    real(real64) :: derivative
+    real(real64), intent(in) :: t, y
+  end function
+end interface
+
+real(real64), parameter :: T_0 = 100, T_room = 20, k = 0.07, a = 0, b = 100, &
+    h(3) = [2.0, 5.0, 10.0]
+
+integer :: i
+
+! loop over all step sizes
+do i = 1, 3
+  call euler(newton_cooling, T_0, a, b, h(i))
+end do
+
+contains
+
+! Approximates y(t) in y'(t) = f(y, t) with y(a) = y0 and t = a..b and the
+! step size h.
+subroutine euler(f, y0, a, b, h)
+  procedure(derivative) :: f
+  real(real64), intent(in) :: y0, a, b, h
+  real(real64) :: t, y
+
+  if (a > b) return
+  if (h <= 0) stop "negative step size"
+
+  print '("# h = ", F0.3)', h
+
+  y = y0
+  t = a
+
+  do
+    print *, t, y
+    t = t + h
+    if (t > b) return
+    y = y + h * f(y, t)
+  end do
+end subroutine
+
+
+! Example: Newton's cooling law, f(T, _) = -k*(T - T_room)
+function newton_cooling(T, unused) result(dTdt)
+  real(real64) :: dTdt
+  real(real64), intent(in) :: T, unused
+  dTdt = -k * (T - T_room)
+end function
+
+end program