Runge-Kutta method: Difference between revisions

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 =={{header|Fortran}}==
 <lang fortran>program rungekutta
-implicit none
-real(kind=kind(1.0D0)) :: t,dt,tstart,tstop
-real(kind=kind(1.0D0)) :: y,k1,k2,k3,k4
-tstart =0.0D0 ; tstop =10.0D0 ; dt = 0.1D0
-y = 1.0D0
-t = tstart
-write(6,'(A,f4.1,A,f12.8,A,es13.6)') 'y(',t,') = ',y,' Error = '&
-           &,abs(y-(t**2+4.0d0)**2/16.0d0)
-do; if ( t .ge. tstop ) exit
-   k1 = f (t           , y                 )
-   k2 = f (t+0.5D0 * dt, y +0.5D0 * dt * k1)
-   k3 = f (t+0.5D0 * dt, y +0.5D0 * dt * k2)
-   k4 = f (t+        dt, y +        dt * k3)
-   y = y + dt *( k1 + 2.0D0 *( k2 + k3 ) + k4 )/6.0D0
-   t = t + dt
-   if(abs(real(nint(t))-t) .le. 1.0D-12) then
-      write(6,'(A,f4.1,A,f12.8,A,es13.6)') 'y(',t,') = ',y,' Error = '&
-           &,abs(y-(t**2+4.0d0)**2/16.0d0)
-   end if
-end do
-contains
-  function f (t,y)
     implicit none
+    integer, parameter :: dp = kind(1d0)
-    real(kind=kind(1.0D0)),intent(in) :: y,t
-    real(kind=kind(1.0D0)) :: f
+    real(dp) :: t, dt, tstart, tstop
+    real(dp) :: y, k1, k2, k3, k4
-    f = t*sqrt(y)
-  end function f
+    tstart = 0.0d0
-end program rungekutta
+    tstop = 10.0d0
-</lang>
+    dt = 0.1d0
+    y = 1.0d0
+    t = tstart
+    write (6, '(a,f4.1,a,f12.8,a,es13.6)') 'y(', t, ') = ', y, ' error = ', &
+        abs(y-(t**2+4.0d0)**2/16.0d0)
+    do while (t < tstop)
+        k1 = dt*f(t, y)
+        k2 = dt*f(t+dt/2, y+k1/2)
+        k3 = dt*f(t+dt/2, y+k2/2)
+        k4 = dt*f(t+dt, y+k3)
+        y = y+(k1+2*(k2+k3)+k4)/6
+        t = t+dt
+        if (abs(nint(t)-t) <= 1d-12) then
+            write (6, '(a,f4.1,a,f12.8,a,es13.6)') 'y(', t, ') = ', y, ' error = ', &
+                abs(y-(t**2+4)**2/16)
+        end if
+    end do
+contains
+    function f(t,y)
+        real(dp), intent(in) :: t, y
+        real(dp) :: f
+        f = t*sqrt(y)
+    end function f
+end program rungekutta</lang>
 {{out}}
 <pre>