In Maple, how do I plot the solutions to a second-order system of ordinary differential equations (ODEs) in the phase plane?
In Maple, use DEtools[DEplot] to plot the solutions to a second-order system of ordinary differential equations (ODEs) in the phase plane. There are alternative methods, but this is usually the best. Following is an example:
> eq1 := diff(v1(t), t) + v1(t) + 2*v2(t) = cos(t); > eq2 := diff(v2(t), t) - 2*v1(t) + v2(t) = sin(2*t); > init1 := v1(0) = 0; > init2 := v2(0) = 0;# [1] Use built-in tool for [numerical] plotting:
> with(DEtools); > DEplot( {eq1, eq2}, [v1(t), v2(t)], 0 .. 3*Pi, {[0, 0, 0]}, scene=[v1, v2], stepsize=.1); ------------# [2] Solve numerically, plot solution:
> soln := dsolve( {eq1, eq2, init1, init2}, {v1(t), v2(t)}, numeric): > V1 := proc(x) subs( soln(x), v1(t) ) end: > V2 := proc(x) subs( soln(x), v2(t) ) end: > plot( ['V1(t)', 'V2(t)', t=0 .. 3*Pi] );# Note use of the single quotes, to delay evaluation.
# The single quotes may be avoided as follows, at a small cost:
> plot( [V1, V2, 0 .. 3*Pi] ); ----------- > readlib(unassign): unassign(v1, v2);# Note: after [2], you must unassign v1 and v2 before the following # will work.
# [3] Solve analytically (if possible), and plot solution:
> solns := dsolve( {eq1, eq2, init1, init2}, {v1(t), v2(t)} ); > assign(solns); > plot( [v1(t), v2(t), t=0 .. 3*Pi] ); ------------For more about statistical and mathematical software, email the UITS Stat/Math Center, visit the center's web page, or phone 812-855-4724 (IUB) or 317-278-4740 (IUPUI). The center is located in Bloomington at 410 N. Park Avenue, and is open for consultation by appointment Monday-Friday 9am-5pm.
Last modified on May 16, 2011.
