Chapter 11. More Fortran Elements: Functions and Subroutines 11.1 ...

11.3.3 Subroutine Example
The use of a subroutine in Fortran will be illustrated with the example of the Verlet
algorithm. Recall from Chapter 5 and Assignment 1 that the velocity Verlet algorithm for
numerically approximating solutions to Newton’s equations of motion is
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x n+1 = x n + v n Δt + 1
2 a n Δt
( )2 . (11.2)
vn+1 = vn + 1
2 an + a ( n+1)Δt
. (11.3)
A subroutine written to carry out N steps of the Verlet algorithm for the harmonic oscillator is given
below. The number of points, time step size, harmonic oscillator force constant, mass, and initial
position and initial velocity
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are the variables passed to the subroutine. The subroutine returns two
arrays, the position and velocity as functions of time.
SUBROUTINE VERLET(N, DT, K, M, X0, V0, X, V)
IMPLICIT NONE
INTEGER N, I
REAL*8 DT, K, M, X0, V0, A1, A2, X(N), V(N)
X(1) = X0
V(1) = V0
DO 100 I = 2, N
A1 = –K*X(I–1)/M
X(I) = X(I–1) + V(I–1)*DT + 0.5*A1*DT**2
A2 = –K*X(I)/M
V(I) = V(I–1) + 0.5*(A1+A2)*DT
100 CONTINUE
RETURN
END
All the variables passed from the main program to the subroutine as well as any others used
within the subroutine must be defined in the variable declaration statement. As was the case for
external function, the variable names used in the subroutine argument list are dummy variables. The
same names do not have to be used in the main program but their types must match.
The main body of the subroutine carries out multiple iterations of the Verlet equations
(11.2) and (11.3). At the end of the subroutine, the array X contains the position as a function of
time and the array V contains the velocity as a function of time. These arrays are passed back to the
main program. The RETURN statement then sends the program control back to the main program.
An example of a main program that calls the VERLET subroutine is given below. The
values of the step size, number of time steps, force constant, mass, and initial position and velocity
are all input from the screen. The main program then calls the VERLET subroutine to advance the
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