SODE Files

			SODE
                by Dennis J. Darland
               djdarland@qconline.com

SODE.icn is source to a Icon program to generate a Maple (or Icon) program 
to numerically solve either a single ordinary differential equation or a 
system of such equations. Whether "sodemaple.icn" or "sodeicon.icn" is 
included determines whether a Maple or Icon program is generated. sats.txt (for Maple) & sats.icn (for Icon) are libraries copied into the output files. 
The files in the archive may be placed in the directory of your choice, but 
sode must then be run in that directory & the problem files placed there 
as well. 

The output maple code is found in "atomall.txt". (or "atomall.icn" for icon)
It is read into maple with 
the command 

read `c:\\path\\atomall.txt`;

Or compiled as usual wirh icon or unicon.

Then start the sode solver with "main();" within Maple.

It has been tested with Maple 7. There was a problem 
in Maple V 4.

The input file is found in a "---.ode"(in Maple) file (or "---.ide"(in Icon)
 file).  There are many in this zip file.
The format is below


Icon can be found at: http://www.cs.arizona.edu/icon/
Unicon can be found at: http://unicon.sourceforge.net/index.html
Info on Maple is at: http://www.maplesoft.com/products/maple/


Format of  .ode file:
----------------------------------
ode spec
$
constants spec
$
initial values
$
exact_soln_y := proc(x) # analytic solutiion to be numerically compared.
(or procedure exact_soln_y(x) for icon. 
---
Any other functions( user defined)
$

------------------------------------
The ode spec is of the form
diff(y,x,N) = x * sin(x);
The operations + - / * are supported.

The functions which may be used are 

ln
exp
sin
cos
tan
sinh
cosh
tanh
arcsin
arccos
arctan
Si(not in Icon)
erf(not in Icon)
expt(a,b) (a to b power.)

Positive literals may also be used.
M1 can be used for -1.

diff (y,x,M) for M < N  & M >= 0
can be used for the lower derivatives of y.
The 0th derivative of y is y itself.

------------------------------------------
SAMPLE .ide file
--------------------------------------------
diff ( y1 , x , 6 ) = 3 * diff( y1, x , 1)  - 2* diff( y2, x, 2);
diff ( y2 , x , 3 ) = 2* diff( y1, x , 2)  - 2 * diff( y3, x, 2);
diff ( y3 , x , 3 ) = 2* diff( y1, x , 5)  - 2 * diff( y2, x, 0);
$
MAX_TERMS:=30;
$
H := 0.0001;            #initial H
x_start := 3.0;         #initial x
x_end := 3.0003;        #final x
y1_init[1] := 1;        #initial value of y1
y1_init[2] := 2;        #initial value of y1'
y1_init[3] := 0.7;      #etc.
y1_init[4] := 1.7;
y1_init[5] := 0.6;
y1_init[6] := 0.9;
y2_init[1] := 9.6;
y2_init[2] := 6.5;
y2_init[3] := 8.5;
y3_init[1] := 6.8;
y3_init[2] := 6.5;
y3_init[3] := 3.5;
max_err := 10e-10; # not implemented well yet
HMIN := 0.00001;    # minimum H
HMAX := 1.0;        # maximum H
adjust_h := 1;      # whether to adjust H (1 is true.  0 is false.)
x_disp_incr := 0.1; # interval between which data is printed 
                             # regardless of H.(This is x... even if the independent variable is different)
MAX_ITER := 100;     # Maximum number of iterations of main loop.
DELTA := 1.0e-10;    # discrimination for display purposes.
Digits := 50;       # Digits -- works only in maple.
$
procedure exact_soln_y1(x) 
return 0.0; # this solution is unknown.
end
procedure exact_soln_y2(x)
return 0.0; # this solution is unknown.
end
procedure exact_soln_y3(x)
return 0.0; # this solution is unknown.
end
$