Hi there,

So my problem is to find the solution(s) of a 3-D system. I can get Maple to spit out a solution (at times), but I am looking for reassurance that this is indeed the solution (if unique, and if not what the other solutions may be). Increasing Digits makes Maple "lose" the solution and return a blank-- normal behavior? Looking at the 3-D plot of the system offers something to puzzle over.

I set up the system in  (x,c,q):

xd := x^.5-.1*x-c;
cd := (.5/x^.5-.1-q)*c;
qd := -(q-.2e-1)*(q-.3e-1)+(q-.25e-1)*(.5/x^.5-.1-q)*c/(x^.5-.1*x-c);
 

I look for a solution with fsolve:

Digits:=10: interface(displayprecision=10):
ss:= fsolve({xd,cd/c,qd}, {x,c,q}, avoid={x=0, c=0, q=0});
xs:=subs(ss,x): cs:=subs(ss,c): qs:=subs(ss,q):

Maple gives:

ss := {c = 2.399289639, q = .2511089584e-1, x = 15.97164840}

If I raise digits to 15, Maple can't solve it anymore. Perhaps this is normal behavior.

I'd like some reassurance that this solution is indeed a solution. Simply feeding the fsolve output back into the system will not work because of a division by zero:

eval(xd,{x=xs,c=cs,q=qs}); eval(cd,{x=xs,c=cs,q=qs}); eval(qd,{x=xs,c=cs,q=qs});

yields:

0.
-.9597158556e-10
Float(-infinity)

I decided to look at the 3-D plot. The plot of the system suggests that there may be several solutions.

The plot:

plotopts:=style=patchcontour, shading=none,lightmodel=light3,axes=boxed:
px:=implicitplot3d({xd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=brown): pc:=implicitplot3d({cd/c}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=green):
pq:=implicitplot3d({qd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=blue):
display3d({pq}, orientation=[-25,70]);
display3d({px,pc,pq}, orientation=[95,90], projection=1);

plot of third equation
plot of 3-D system

The plot is not very clean, and no matter how hard I've tried, by turning it around and zooming near the Maple solution, it is not clear that there are no other solutions. (well perhaps it is clear from the equations themselves, but I couldn't work it out and resorted to the numerical approach)

Does somebody have a sheet covering that algorithm for continous
anti-derivatives of rational functions (Bronstein's book §2.8
"Integration of transcendental functions")?

Or can show me, how to extract it from Maple's library in case
it is there (and I guess Maple covers that ...) for explicite
use?

Hello,

I am trying to change the variable in an integral and I have two problems with it:

My first problem is that I can't get the integrand of the new integral with GetIntegrand when I use IntegrationTools[Change] :

restart;

a1:=Int(1/(2*A),x=-A..A);

D1:=IntegrationTools[Change](a1,x=20*log[10](u));

View 8939_simplify_CRRA.mw on MapleNet or Download 8939_simplify_CRRA.mw
View file details

Dear all:

    I am wondering if there is any way in Maple you can do prettyprint with the printf?  Printf gives me more power but the output format of printf is "C-style". For example,

f := exp(x) + 3*sqrt(exp(x));

f1 := subs(exp(x)=y,f);

printf("Transformation is %a s.t %a => %a\n", f,f1 );

gives a display which is very hard to read. Is there any way to do a prettyprint with this kind of things?

Thanks,

Peter

Hi all,

I have a function defined as a sum:

with(PDEtools): mfx:=(x,y,ufx)->sum(ufx[k]*(x-x[k])*(y-y[k]),k);

I want to declare mfx(x,y,ufx) so that it would appear as mfx in subsequent displays. However, when I tried

declare(mfx(x,y,ufx));

Maple tells me that "Error, (in PDEtools:-declare) cannot declare objects as sum(ufx[k]*(x-x[k])*(y-y[k]), k)".

How can I solve this problem?

Thanks.

I am having a problem differentiating a function. I have a fluid in a channel with moving walls corresponding to y=a(t) (upper wall) and y=-a(t) (lower wall). The fluid is driven by suction out of the walls. The speed of the fluid being sucked out of the walls is the constant v_w. I am using the variable eta=y/a(t) to model the fluid. y is the normal direction to teh channel and x is the streamwise direction of the channel. So I have

x=streamwise direction of the channel

y=normal direction of the channel

a(t)=height of the channel

v_w=constant

This is inspired by MapleTA, but applies to Maple in general.  According to the documentation, bitmap plot devices do not allow for font selection, meaning the recommended textplot(...,font=[SYMBOL]) fails to render greek characters such as π in plots which are rendered for embedding in web pages.  This seems like a gaping omission, so we're hoping we've just missed something here.  Is there any way to get the symbol for pi onto a jpeg or gif plot?

Hi all,

I have little (almost zero) experience with Maple. Nonetheless I wish to use Maple 8 to solve a set of 5 equations for 8 unknowns.

At the moment my strategy is to input each equation, make a set of the 5 equations, and then use the 'solve' command to determine the variables. I then refine the answer using 'allvalues' and 'evalf'. Is this the best approach?

Any help or guidance on this is greatly appreciated.

I'm a brand new user. 

Maple 12, Windows Vista, Integration Tutor.

When viewing the steps in the solution, Maple does it's own u-subs ("change of variable").  Is there any way to see what it is setting "u=?"?

It's very difficult to follow the steps when I can't tell what it's subbing out.

Also, within the same tutor, it doesn't seem to like to intigrate to infinity.  It tells me "...infinity should be a number."  ! ? ! ?

Thank you in advance.

Jim Z

Hello,

I have an expression:

y:=a*10^(x/20)+b*10^(x/10);

(x is real here)

I 'd like to write this epxression in the form of y=a*K+b*K^(2) with Maple using 10^(x/20)=K substitution.

I have tried it with subs and algsubs but they don't work here for me.

(Originally I had a more complicated expression of this type).

Thanks for your help in advance.

Hello Maple wizards,

I'm trying to use numapprox[infnorm] to locate the L-infinity norm of functions such g(y) on the range 0.0..1.0 at the bottom of this post. Plotting shows that the function has an range of width 10e-3 that contains a minimum near y=0.9965, but infnorm() doesn't find it unless the range is artifically constrained to be close to the minimum.  I'm using infnorm() in a proc's loop, so manual control of the range based on the graph is not an appealing option.

Suppose you have a system of linear ODE's and you want to convert them into one matrix equation. Basically what you do with algebraic eqs using GenerateMatrix. Is there a Maple command to do that? Obviously, one could you use the lagrangian if the eqs happen to represent a dynamic system but that's not what I am looking for. And the second part of the question, once you have the matrices is there a way to export them and ,say, run a finite element analysis with them?

thanks a lot

dimitrios