From octave-sources-request at bevo dot che dot wisc dot edu  Sun May 24 20:20:35 1998
Subject: Tests for dassl and lsode functions
From: "Billinghurst, David" <David dot Billinghurst at riotinto dot com dot au>
To: "'octave-sources at bevo dot che dot wisc dot edu'" 	 <octave-sources@bevo.che.wisc.edu>
Date: Mon, 25 May 1998 11:17:56 +1000

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Here are a couple of tests for diffeq.

+++++++++++++++++++++++++++++++++++++++++
(Mr) David Billinghurst
Comalco Research and Technical Support
PO Box 316, Thomastown, Vic, Australia, 3074
Phone:	+61 3 9469 0642
FAX:	+61 3 9462 2700
Email:	David dot Billinghurst at riotinto dot com dot au


 <<dassl-1.m>>  <<dassl-2.m>>  <<lsode-1.m>> 

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	name="dassl-1.m"
Content-Disposition: attachment;
	filename="dassl-1.m"

# dassl-1.m
#
# Test dassl() function
#
# Author: David Billinghurst (David dot Billinghurst at riotinto dot com dot au)
#         Comalco Research and Technology
#         20 May 1998
#
# Problem
#
#    y1' = -y2,   y1(0) = 1
#    y2' =  y1,   y2(0) = 0
#
# Solution
#
#    y1(t) = cos(t)
#    y2(t) = sin(t)
#
#
x0=[1,0];
xdot0=[0,1];
t=[0:1:10];
tol=100*dassl_options("absolute tolerance");

function res = f( x, xdot, t)
  res = zeros(2,1);
  res(1) = xdot(1) + x(2);
  res(2) = xdot(2) - x(1);
endfunction

function y = soln(t)
  y1 = cos(t);
  y2 = sin(t);
  y = [y1;y2]';
endfunction

[x,xdot] = dassl("f",x0,xdot0,t);
y = soln(t);
all(all( abs(x-y) < tol ))

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	name="dassl-2.m"
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	filename="dassl-2.m"

# dassl-2.m
#
# Test dassl() function
#
# Author: David Billinghurst (David dot Billinghurst at riotinto dot com dot au)
#         Comalco Research and Technology
#         20 May 1998
#
# Based on SLATEC quick check for DASSL by Linda Petzold
#
# Problem
#
#   x1' + 10*x1 = 0,   x1(0) = 1
#   x1  + x2    = 1,   x2(0) = 0
# 
#
# Solution
#
#  x1(t) = exp(-10*t)
#  x2(t) = 1 - x(1)
#
x0=[1,0];
xdot0=[-10,10];
t=[0:0.2:1];
tol=500*dassl_options("absolute tolerance");

function res = f( x, xdot, t)
  res = zeros(2,1);
  res(1) = xdot(1) + 10*x(1);
  res(2) = x(1) + x(2) - 1;
endfunction

function y = soln(t)
  y1 = exp(-10*t);
  y2 = 1 - y1;
  y = [y1;y2]';
endfunction

[x,xdot] = dassl("f",x0,xdot0,t);
y = soln(t);
all(all( abs(x-y) < tol ))

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Content-Type: application/octet-stream;
	name="lsode-1.m"
Content-Disposition: attachment;
	filename="lsode-1.m"

# dassl-1.m
#
# Test lsode() function
#
# Author: David Billinghurst (David dot Billinghurst at riotinto dot com dot au)
#         Comalco Research and Technology
#         20 May 1998
#
# Problem
#
#    y1' = -y2,   y1(0) = 1
#    y2' =  y1,   y2(0) = 0
#
# Solution
#
#    y1(t) = cos(t)
#    y2(t) = sin(t)
#
x0=[1,0];
xdot0=[0,1];
t=[0:1:10];
tol=500*lsode_options("absolute tolerance");

function xdot = f( x, t)
  xdot    = zeros(2,1);
  xdot(1) = -x(2);
  xdot(2) =  x(1);
endfunction

function y = soln(t)
  y1 = cos(t);
  y2 = sin(t);
  y = [y1;y2]';
endfunction

x = lsode("f",x0,t);
y = soln(t);
all(all( abs(x-y) < tol ))

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