usode
                by Dennis J. Darland
              dennis.darland@yahoo.com
         http://www.dennisdarland.com/index.html

usode.icn is source to a Unicon program to generate a Unicon program 
to numerically solve either a single ordinary differential equation or a 
system of such equations. 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 command "make name=sin" would
solve the problem in "sin.ude" The basic problems are solved by the script
"test.basic" Also the APFP class files & unicon & unicon overloaded operators
are required.  See http://sode.sourceforge.net/index.html  

The output unicon code is found in "diffeq.icn".
Use "make name=your_problem.ude" to build & run it.

The problem file is found in a "---.ude" file.
There are many in the usode??tar.gz file.
The format is below

Unicon can be found at: http://unicon.sourceforge.net/index.html
APFP can be found at http://sourceforge.net/projects/apfp/

Format of  .ude file:
----------------------------------
ode spec
$
constants spec
$
initial values
$
procedure exact_soln_y(x) for icon. # analytic solutiion to be numerically compared.
---
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.

------------------------------------------
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 * y2;
$
MAX_TERMS:=30;          # Max Number of Taylor series terms
MIN_TERMS:=11;          # Min Number of Taylor series terms
$
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;

log10relerr := -6.0; #log base 10 of relative eror permittd default = -8.0;
log10abserr := -6.0; #log base 10 of absolute eror permittd default = -8.0;

HMIN := 0.00001;   # minimum H
HMAX := 1.0;       # maximum H
adjust_h := 1;     # whether to adjust H (1 is true.  0 is false.)
look_poles := 1;   # whether to estimate singularities(1 is true.  0 is false.)
disp_incr :=0.1 # 0 for endpoints only -1 for "natural" H   
MAX_ITER := 100;     # Maximum number of iterations of main loop.
MAX_HOURS := 0;     # Maximum number of hours to execute - # 0 default
MAX_MINUTES := 15;     # Maximum number minutes to execute - # 15 default
SMALL_FLOAT := 1.0e-200;   #default
SMALLISH_FLOAT := 1.0e-10;   #default
LARGE_FLOAT := 1.0e100;   #default
ALMOST_1 := 0.99;  #default
PROGRESS_IND := 10; #iterations between progress output # 10 default
$
procedure exact_soln_y1(x) 
return ZERO; # this solution is unknown.
end
procedure exact_soln_y2(x)
return ZERO; # this solution is unknown.
end
procedure exact_soln_y3(x)
return ZERO; # this solution is unknown.
end
$