Arjen Markus (5 march 2009) Yesterday I spoke with Kevin Kenny and Cameron Laird about the possibilities of developing an application a la XPPAUT ([L1 ]). The idea is to use such packages as Tclode and Plotchart to solve systems of ordinary differential equations and plot the results.
These equations should be definable in a very similar way as XPPAUT allows. The user-interface should be much more modern though.
Anyway, here is a very first (or should I say zeroth) shot at something like that. I have called it "Bernoulli" in honour of those great 17th-century mathematicians, Johan, Jacob and Daniel. (it is also a bit of nostalgia for me, as some 15-20 years ago I developed a similar program, also called bernoulli).
All it does now is present the graph of a function you define as an expression ...
# bernoulli.tcl --
# Integrate systems of ordinary differential equations
#
#package require Tcl 8.5
package require Tk
package require Plotchart
# plotf --
# Convenience procedure to plot a function of one variable
#
# Arguments:
# range Range over which to plot the function (x-axis)
# expression Expression by which the function is defined
# (independent variable: t)
#
proc plotf {range expression} {
# Very simple for now: no parameters
foreach {tmin tmax} $range {break}
set nosteps 100
set tstep [expr {($tmax-$tmin)/double($nosteps)}]
if { ![winfo exists .c] } {
pack [canvas .c]
} else {
.c delete all
}
set tvalues {}
set xvalues {}
set xmin {}
set xmax {}
for {set i 0} {$i < $nosteps+1} {incr i} {
set t [expr {$tmin + $i*$tstep}]
set x [expr $expression]
lappend tvalues $t
lappend xvalues $x
if { $xmin == {} || $x < $xmin } {
set xmin $x
}
if { $xmax == {} || $x > $xmax } {
set xmax $x
}
}
set tscale [::Plotchart::determineScale $tmin $tmax]
set xscale [::Plotchart::determineScale $xmin $xmax]
set p [::Plotchart::createXYPlot .c $tscale $xscale]
foreach t $tvalues x $xvalues {
$p plot function $t $x
}
}
# main --
# Test the stuff
#
plotf {0 10} {exp(-$t)*cos(2.0*$t)}
after 3000 {
plotf {0.0001 100} {sin($t)/$t} ;# Avoid t=0 of course
}