## 294 Reputation

14 years, 241 days

## I know...

I know what is the wrong.

in the f := d*t8(x, y)/h+E*s(x, y)/R^2+p*R*t4(x, y)/h

I made a mistake.

I am sorry to trouble everyone

To detail explain what I want to do

There are two formula

1ST:Matrix(2, 2, {(1, 1) = -k, (1, 2) = -c*omega, (2, 1) = c*omega, (2, 2) = -k})*Vector(2, {(1) = A2, (2) = B2})=Matrix(2, 2, {(1, 1) = M*omega^2-K-k, (1, 2) = -c*omega, (2, 1) = c*omega, (2, 2) = M*omega^2-K-k})*Vector(2, {(1) = A1, (2) = B1})+Vector(2, {(1) = 0, (2) = F})

2RD:Matrix(2, 2, {(1, 1) = -k, (1, 2) = -c*omega, (2, 1) = c*omega, (2, 2) = -k})*Vector(2, {(1) = A1, (2) = B1})=Matrix(2, 2, {(1, 1) = m*omega^2-k, (1, 2) = -c*omega, (2, 1) = c*omega, (2, 2) = m*omega^2-k})*Vector(2, {(1) = A2, (2) = B2})

I want to use Vector(2, {(1) = A1, (2) = B1}) to show Vector(2, {(1) = A2, (2) = B2})

but after the order ,maple do nothing.

Maybe there is something wrong in it.

Thank you.

## success...

I am really appreciate of you.

You are so smart!

## open...

In your way, I open the worksheet. I am very pleasure to do it.

I ran whole file, but only the muller.mw shows error, others are right. Such as

Muller's Method

restart;
libname:="c:/nalib",libname;
"c:/nalib", "C:\Program Files\Maple 12/lib"
with(numanal);
Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received numanal

r1:=muller(p,-13,-12,-11,.000001,100,r1);
Error, recursive assignment
Success!  Now lets continue to the other real roots.
r2:=muller(p,-1,0,1,.000001,100,r2);
Error, recursive assignment
Again success.
r3:=muller(p,1,2,3,.000001,100,r3);
Error, recursive assignment
A third success. Now let's go for the complex roots.  It's quite a bit harder to pick three sensible values because we don't have the graph to help us.  But we will pick three complex numbers.
r4:=muller(p,1+I,2+2*I,3+3*I,.000001,100,r4);
Error, recursive assignment
Treating
1.41102 ^(10, -14)
as 0, this is just the third root, so we try again.
r4:='r4';
r4
r4:=muller(p,3+5*I,8-4*I,7+5*I,.000001,100,r4);
Error, recursive assignment
Treating
-5.288 ^(10, -16)
as 0, this is just the third root, so we try again.
r4:='r4';
r4
r4:=muller(p,15+5*I,8-14*I,7+15*I,.000001,100,r4);
Error, recursive assignment
Success!  For the fifth root, we again take the conjugate of the fourth root.
r5:=conjugate(r4);
__
r4
Just to show you can find complex roots with real first approximations, we try to find
r4
with real first approximations.
r4:='r4';
r4
r4:=muller(p,15,8,7,.000001,100,r4);
Error, recursive assignment
Success!

And by the way, I am using Maple 12. How to solve it?

Thank you very much.

## about the worksheet...

I am so sorry, I am the beginning of Maple, uptill now I can not use the worksheet.

I copy the worksheet mulleralg.mw(frome up worksheet to down worksheet) from http://www.cbu.edu/~wschrein/media/ANA/muller.mw and press Enter, but the time is running without end and nothing can be done. And then I tried to use the worksheet only from the first <worksheet> to <styles> and Maple shows

Error, invalid argument sequence
(Version majorequals"13" minorequals"0"Typesetting:-mambiguous(sol ,

Typesetting:-merror(invalid argument sequence)))     (Labeluminus0Scheme

valueequals"2" prefixequals"" sol)     (Viewuminus0Properties presentation

equals"false" sol)     (MapleNetuminus0Properties warnlevelequals"3"

longdelimequals"true" plotoptionsequals"" echoequals"1" errorcursorequals

"false" elisiontermsthresholdequals"10000" elisiontermsbeforeequals"100"

errorbreakequals"1" prettyprintequals"2" promptequals">" latexwidthequals

"6.0" useclientjvmequals"true" ansiequals"false" screenheightequals"25"

labelwidthequals"20" plotdeviceequals"inline" typesettingequals"standard"

displayprecisionequals"-1" indentamountequals"4" elisiondigitsthreshold

equals"10000" quietequals"false" plotoutputequals"terminal" rtablesizeequals

"10" preplotequals"" showassumedequals"1" plotdriverequals"openviz"

elisiontermsafterequals"100" labellingequals"true" postplotequals""

screenwidthequals"79" elisiondigitsbeforeequals"100" elisiondigitsafter

equals"100" verboseprocequals"1" imaginaryunitequals"I" ShowLabelsequals

"false" sol)

and then define p and > muller(p, -13, -12, -11, 0.1e-5, 100, r1);

it only shows Error, recursive assignment

I am so sorry to trouble you again and again, thank you very much.

## but...

I am so sorry,I did what you have told me, but it shows as follows

> restart; p := x^5+11*x^4-21*x^3-10*x^2-21*x-5;
5       4       3       2
x  + 11 x  - 21 x  - 10 x  - 21 x - 5

> muller(p, -13, -12, -11, 0.1e-5, 100, r1);
/ 5       4       3       2                                             \
muller\x  + 11 x  - 21 x  - 10 x  - 21 x - 5, -13, -12, -11, 0.000001, 100, r1/

> muller(p, -13, -12, -11, 0.1e-5, 100, 'r1');
/ 5       4       3       2                                             \
muller\x  + 11 x  - 21 x  - 10 x  - 21 x - 5, -13, -12, -11, 0.000001, 100, r1/

> muller(p(x), -13, -12, -11, 0.1e-5, 100, r1);
/    5          4          3          2
muller\x(x)  + 11 x(x)  - 21 x(x)  - 10 x(x)  - 21 x(x) - 5, -13, -12, -11,

\
0.000001, 100, r1/

I think it should work.But there is no result. I donot know what is the matter. I am using Maple 12.

Thank you very much

Thank you

## renew...

the formula I want to show is in the PDF file I have uploaded(because it is a little difficult to write here),and in Maple I do,

hh := proc (`&varpi;`) options operator, arrow; (`&varpi;`-V*m*Pi/LL)^2/C[f]^2-m^2*Pi^2/LL^2 end proc; H := proc (`&varpi;`) options operator, arrow; piecewise(0 <= hh(`&varpi;`), sqrt(hh(`&varpi;`)), hh(`&varpi;`) < 0, sqrt(-hh(`&varpi;`))) end proc; Y := proc (`&varpi;`) options operator, arrow; piecewise(0 <= hh(`&varpi;`), BesselJ(n, R*sqrt(hh(`&varpi;`))), hh(`&varpi;`) < 0, BesselI(n, R*sqrt(-hh(`&varpi;`)))) end proc; YY := proc (`&varpi;`, z) options operator, arrow; piecewise(0 <= hh(`&varpi;`), BesselJ(n, z), hh(`&varpi;`) < 0, BesselI(n, z)) end proc; www := proc (`&varpi;`) options operator, arrow; (D[2](YY))(`&varpi;`, R*sqrt(hh(`&varpi;`))) end proc; PF := proc (`&varpi;`) options operator, arrow; rho[f]*(`&varpi;`-V*m*Pi/LL)^2*Y(`&varpi;`)/(H(`&varpi;`)*www(`&varpi;`)) end proc

Now I am not sure whether it is right or not, can you help me?

Thank you

## Thank you...

thank you very much

## thank you all...

I will try other method, after doing that I will post it here.

Thank you all very much

## thank you...

thank you, I will try other methods

Maybe I should use another way to get the solution of this equation for omega.

Would you like to  give me some advice?

Thank you very much

## the same...

I met the same problem today,I use maple13,how t solve it

## I know the reason...

because the w has more than one reslut,so it can not draw the pic

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