Trouble with global vars

[Tony Mullins]

I am getting the following errors when attempting to use the builtin
quad function to integrate a scalar integrand.  If I set the values of
the global variables position, time and sum_limit at the octave
command line and call the function integrand directly I get no such
error.  The .m files follow the error message.

Tony Mullins                            |internet: address@hidden
Dept. of Chem. Eng'rg., CPE 5.438       |ma bell : 512-471-1024
University of Texas - Austin            |ma FAX  : 512-471-7060
Austin, TX  78712-1062                  |Home sweet home: 512-467-0126

> octave integral_soln.m
Octave, version 1.1.1.
Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton.
This is free software with ABSOLUTELY NO WARRANTY.
For details, type `warranty'.

error: `tau' undefined near line 14 column 48
error: evaluating expression near line 14, column 48
error: evaluating binary operator `*' near line 14, column 46
error: evaluating argument list element number 0
error: evaluating index expression near line 14, column 31
error: evaluating binary operator `+' near line 14, column 29
error: evaluating assignment expression near line 14, column 16
error: evaluating for command near line 11, column 3
error: called from `integrand' in file `/home/jamull/octave/integrand.m'
error: evaluating argument list element number 0

******************** integral_soln.m ********************
# This file computes the solution to the 1D diffusion equation
# on 0<x<1 using the result from the boundary integral technique.
# It is used in conjunction with the function integrand(tau) and
# calls the Octave function quad("f", a, b, tol, sing) to perform
# the integration.
  
global position time sum_limit;
x = linspace(0,1,100);
time = .025;
lower_limit = 0;
upper_limit = time;
singularity = time;
sum_limit = 100;

for i = 1:length(x)
  position = x(i);
  y(i) = quad(integrand,lower_limit,upper_limit,singularity);
endfor

******************** integrand.m ********************
function int_grand = integrand(tau)
  # This function computes the integrand in the time-convolution
  # integral for the boundary integral solution to the 1-D diffusion
  # equation on 0<x<1.
  # These global variables are necessary because the quadrature
  # routines do not provide for parameter communication.
  
  global position time sum_limit;
  
  exp_series = 1;
  for i = 1:sum_limit
    lambda = (2*i+1) * pi;
    lambda_sq = lambda*lambda;
    exp_series = exp_series + exp(-lambda_sq * tau);
  endfor
  
  den_1 = 4*(time-tau);
  rt_den_1 = sqrt(den_1*pi);
  den_2 = den_1 * den_1 * den_1;
  rt_den_2 = sqrt(den_2*pi);
  x_sq = position*position;
  x_minus_1 = position-1;
  x_minus_1_sq = x_minus_1 * x_minus_1;
  int_grand = position*exp(-x_sq/den_1);
  int_grand = (int_grand - x_minus_1*exp(-x_minus_1_sq/den_1))/rt_den_2;
  int_grand = 2*int_grand + 4*exp_series* (exp(-x_sq/den_1) ...
      + exp(-x_minus_1_sq/den_1))/rt_den_1;
endfunction