MaplePrimes - answers and comments on Question, dsolve problem with plotting acceleration

two ways

Adri vanderMeer van der Meer — Thu, 03 May 2012 17:47:14 Z

First possibility: you want to plot the derivative of x'(t), that is to say: the derivative of a numeric procedure. I suppose that odeplot is not designed for that. So use the option output=listprocedure:

sol3 := dsolve({DE1, DE2, ICs}, numeric, output=listprocedure );
v := subs(sol3,diff(x(t),t));
st := time(): plot(D(v),0..3); T := time() - st;

Faster is to calculate timeseries for x(t) and v(t) and use a(t) from the differential equation:

solve( DE1, diff(diff(x(t), t), t) ): subs( {m(t)=m, x(t)=x, diff(x(t),t)=v}, % ):
a := unapply( %, t,m,x,v );     #acceleration as a function of t, m, x and x'
sol2 := dsolve({DE1, DE2, ICs}, numeric, output=Array([seq(i,i=0..3,0.001)]) );
   # sol2 has two parts: a list with the names of the variables and a matrix of calculated values
plot( <sol2[2,1][1..-1,1]|a~(seq(sol2[2,1][1..-1,i], i=1..4))> );

a(t)

acer — Thu, 03 May 2012 22:22:39 Z

Try changing the call to dsolve(...,numeric) to be,

sol1 := dsolve({DE1, DE2, ICs, a(t) = diff(x(t), t, t)}, numeric, range = 0 .. 3);

Then, your last plot could be produced using,

odeplot(sol1, [t, a(t)], 0 .. N);

That could be a way to get better results, numerically. It makes dsolve(...,numeric) compute a(t) itself. By instead using D(v)(t) then when that gets evalf'd Maple will internally call fdiff() to compute a derivative numerically using a multi-point difference scheme. I would expect dsolve(...,numeric) to be able to compute a(t) more robustly than that, in general if not specifically.

acer

forgot to thank you for this. it worked.

Gbrandt — Tue, 08 May 2012 22:37:23 Z

forgot to thank you for this. it worked. your help was much appreciated.