Structure of ODE files

All ODE files are just text files which consist of a series of definitions and directives to the XPP parser. The order in which the definitions are given is usually unimportant with one major exception. So-called fixed or temporary variables are evaluated in the order in which they are defined. Thus, you should never use a named fix variable before it is defined as this will lead to some rather bizarre results when you attempt to solve an ODE. ODE files are all line oriented with a limit of 1024 characters per line. You can use the standard line continuation symbol \ . Here are all the possible ODE file directives:

#: comment line. This is ignored by XPP

'': A comment that is extracted and can be displayed in a separate window.

'' {a=1,b=2,...}: A comment with some ``action'' associated with it. When these comments are displayed in the comment window, an * appears next to them. When clicked by the user, various initial conditions, parameters, and XPP internal options can be set.

!name=formula This defines a derived parameter, name whose values could depend on other parameters. These do not appear in the parameter list since they are presumably tied to the other parameters. Ecah time you change a parameter, they also are updated.

options filename: Insert a file name with common options. This is include only for backward compatibility and is generally obsolete.

name(t+1)=formula or

dname/dt=formula or

name'=formula: Define a differential/difference equation dependent variable, name and the formula defining its right-handside. For example

name(t)=formula or

volterra name = formula: Define a Volterra integral equation for the variable name. For example
y'=-y + a int{exp(-(t-t'))*max(y-1/(1+(t-t')^2),0)}
The # symbol means a convolution and [a] multiplies the integrand by


markov name nstates
{0} {P0,1} ... {P0,N-1}
{P1,0} {0} ... {P1,N-1}
... ... ... ...
{PN-1,0} {PN-1,1} ... {PN-1,N-1}

This defines a Markov variable, name which has nstates states. Then following is the transition table as a series of formulas that are delimited by the curly brackets { } . The diagonal entries are ignored but should still contain a number or formula. For example:
markov z 2
{0} {alpha(v)}
{beta(v)} {0}
defines a two-state Markov process with transition from state 0 to 1 determined by the rate alpha(v) and the transition from 1 to 0 determoined by beta(v)

aux name=formula defines a named quantity, name which appears in the data browser and is available for plotting. Note that auxiliary variables are not known internally to XPP so that you can't use them in formulas

name= formula defines an internal or quantity which can be used in other formulas. This fixed variable serves the same function as temporary quantities in C code.

par name1=value1, name2=value2, ... defines named parameters with default values. These can later be altered and varied in XPP. Never put spaces between the name, value, and equal sign. For example:
par a=1,b=2,c=2,big_g=20

number name1=value1, name2=value2, ... defines named parameters with default values. These are fixed and cannot be changed in XPP. For example:
number faraday=96485,rgas=8.3147,tabs0=273.15

name(x,y,...)=f(x,y,...) defines a function of up to 9 variables. This function can be used in any right-hand side or other functions. For example:

table name filename defines a lookup table called name defined the values found in the file, filename. This behaves as a one variable function which uses linear interpolation on the values of the tabulated file. The file has the structure:
The domain of the function is [xlo,xhi]

table % name npts xlo xhi f(t) defines a precomputed table called name using npts and evaluating f(t) at t=xlo,...,xhi For example:
table h % 101 0 6.283 sin(t)+.6+.4*cos(t)+.2*sin(2*t)
Tables are automatically re-evaluated whenever you change parameters unless you turn off the AUTOEVALUATE flag from within XPP or in the ODE file with
@ autoeval=0

wiener name1, name2, ... defines a series of normally distributed random variables with mean 0 and standard deviation sqrt(dt) where dt is the internal time step. The advantage of using wiener is that when you change the time-step, the magnitude of these variables is automatically adjusted.

global sign condition {name1=form1;...} defines a global flag allowing XPP to implement delta functions. If sign=1 and condition changes from negative to positive or if sign=-1 and condition changes from positive to negative, or if sign=0 and condition vanishes identically, then each of the variables, name is immediately changed to the value of formula. For example:
global 1 x-1 {x=0;y=y+a*sin(y)}

init name1=val1,name2=val2,... sets the initial data of name to the number val.

name(0)= expression sets the initial value of name to the expression. If name is a delay-differential equation variable, then if expression is a function of time, t, then name(t) is set to the function for -M < t < 0 where M is the maximum delay. For example:

bdry expression defines a boundary condition at the start or the end of an interval. If the variable name is primed, then it refers to the end of the interval, otherwise to the start of the interval. For example:
bdry u'-v-1
forces the boundary condition u(L)-v(0)-1=0 where [0,L] is the interval for the ODE.

0= expression defines an algebraic condition for differential-algebric equations.

solve name=expression tells XPP to solve the algebraic conditions for the variable name with initial guess expression. For example:
init x=0
solv y=-.56715
Solves the DAE x'=-y where y+e^y=x Note that there is no closed form inverse of y+e^y.

special name=FUN(...) defines a one-dimensional array name that represents a special summation involving an array of variables and a table. FUN can be one of the following:

These can then be used in right-hand sides of ODEs. For example
table w % 21 -10 10 exp(-abs(t))
special k=conv(even,101,21,w,u0)
Here k evaluates as the discrete convolution of exp(-|x|) with the array u.

set name {x1=z1,x2=z2,...,} defines a named set of declarations including parameter values, initial data, and options, which can be invoked while running XPP with the File Get par set command. For example:
set hopf {a=.3,x=1.2,b=9}

@ opt1=val1,opt2=val2,... sets various internal XPP options. For example:
@ maxstor=100000,total=1000,dt=.02
See OPTIONS for a complete list of options.

anything[j1..j2] expr[j] is expanded by XPP into j2-j1+1 statements e.g.
is expanded into:

%[j1..j2] expands all following statements until another % is encountered as above. For example:
is expanded into:

export {x1,x2,...,xn} {y1,...,yn} sends and receives variables and parameters to and from dynamically loaded libraries. Click here for details.

done tells XPP the file is complete.

Reserved words

You should be aware of the following keywords that should not be used in your ODE files for anything other than their meaning here.
sin cos tan atan atan2 sinh cosh tanh
exp delay ln log log10 t pi if then else
asin acos heav sign ceil flr ran abs del_shft
max min normal besselj bessely erf erfc hom_bcs
arg1 ... arg9  @ $ + - / * ^ ** shift
| > < == >= <= != not \# int sum of i'

These are mainly self-explanatory. The nonobvious ones are: