Items tagged with eigenvalue

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newbie here. When I give Maple 2016.2  a boundary value ODE with an eigenvalue in it, it returns the trivial solution. I was wondering if Maple supports finding non-trivial solution and also give the eigenvalue values associated with the non-trivial solution?

restart;
ode:=diff(y(x),x$2)+lambda*y(x)=0;
bc:=y(0)=0,y(L)=0:
assume(L>0,L,'real'):
sol:=dsolve({ode,bc},y(x));

The outtput is `y(x)=0`

In Mathematica, it gives both trivial and non-trivial solution:

Clear[L0, lam, x, y, r]
ode = y''[x] + lam y[x] == 0;
bc = {y[0] == 0, y[L0] == 0};
sol = Assuming[Element[L0, Reals] && L0 > 0, 
  DSolveValue[{ode, bc}, y[x], x]]

And the answer is

If Maple does not currently support this, any one knows if this will added to Maple 2017?

 

I have a big square matrix(1000*1000) having parameter x within some of its entries.

How do you suggest to find close form eigenvalue of such matrix with maple? (eigenvalue will be function of x)

 

Here is a code

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

Download EQ.mw

A fragment of code

for b in extra_bcs do try print(b = 10^(-2)); res[b] := dsolve(dsys4 union {b = 10^(-2)}, numeric, initmesh = 2024, output = listprocedure, approxsoln = [omega2 = 0.1e-2, s(x) = cosh(upsilon*x)-cos(upsilon*x)-(cosh(upsilon)+cos(upsilon))*(sinh(upsilon*x)-sin(upsilon*x))/(sinh(upsilon)+sin(upsilon)), g(x) = sin(((2*n+1)*(1/2))*Pi)], abserr = 0.1e-1) catch: print(lasterror) end try end do; indx := indices(res, nolist); nops([indx]); res[indx[i]]; seq(subs(res[indx[i]](1), omega2(1)), i = 1 .. nops([indx]))

What's the best way to get the eigenvector associated with a certain eigenvalue?

Specifically, given the nature of my matrix A, I know that there ALWAYS exists an eigenvector with eigenvalue 1.  Is there a quick way to extract this without looping through the output of Eigenvectors() and checking each one?

Hi. I'm hacing trouble writing a maple procedure for the question below, can anyone help?

 

Write a maple procedure which takes as its input the vectoeat u1 and u2 and the eigenvectors lambda1 and lambda2 where u1,u2 are element of R^2 and the lambdas are real numbers.

If u1,U2 is linearly independent then the output is the matrix A an element of R^2x2 with the property that Au1= lambda1u1 and AU2=lambda2u2;

if u1,u2 is linearly dependent then the output is the statement "not an eigenbasis".

 

I I then have two inputs which I have to do but I'm not sure on how to write the procedure. Any help will be much appreciated.  

 

Thanks :)

 

 

Hi!

I am comptuing the eigenvalues and the characteristic polynomial of a 8 by 8 symmetric matrix, say M. Thus, we define the matrix M, and compute its charast. plynm. by

 

 

and its eigenvalues with the command

 

 

Well, Maple returns the charast. polynm. an dthe eigenvalues. But, if we compute p(E[k]), for k=1,...,8, thats is, the values of the polynomial p(x) in the eingenvalues, Maple not turns cero!!! I'm really confused ... anyone know what could be happening?

 

Maple attached file with this example. Thank very much for your help!!

 

Download exam_eigenvalues.mw

hi .how i can calculate eigenvector associated with the eigenvalue of the matrix.for example according attached file below

what are  eigenvector associated with the eigenvalue of matrix q which  determined as (2646.408147, 3142.030259, 6621.757707) respectively??

thanks...

eign.mw 

Hello everyone!

I'd like to as a question that might be very simple, but the thing is that I am completely new to Maple, and I have some homework I need to solve all of a sudden... I tried watching some tutorials and did a lot of search, but I just can't make this one work.
Briefly - my task is to derive the vibrational modal shapes of an annular disk (a circular disk with the center "missing"). So far what I know for sure is, that the radial term of the vibrational deflection is given as a linear combination of 4 types of bessel functions (Jn, Yn, In and Kn) - bessel functions of the 1st and second kind, and modified bessel functions of the 1st and second kind. Something like this:

Rmn(r) = A*Jn(kr) + B*Yn(kr) + C*In(kr) + D*Kn(kr).

Now, I need to find the values for k (the wavenumber), and the coeffitients B, C and D. I don't need coeffitient A, because I'll jus fix that to be 1. To do this, I have the following 4 boundary conditions:

1) Rmn(b) = Jn(kb) + B*Yn(kb) + C*In(kb) + D*Kn(kb) = 0

2) R'mn(b) = k(Jn'(kb) + B*Yn'(kb) + C*In'(kb) + D*Kn'(kb)) = 0

3) R''mn(a) = k2(Jn''(ka) + B*Yn''(ka) + C*In''(ka) + D*Kn''(ka)) = 0

4) R'''mn(a) = k3(Jn'''(ka) + B*Yn'''(ka) + C*In'''(ka) + D*Kn'''(ka)) = 0

So, four equations in four unknowns (k, B, C and D) - and I can't get it to work.

I did the following, and it gives me some totally wrong values (complex wavenumbers and such). Again, I am completely new to Maple, so I might have done something completely silly without even noticing...

b := 0.17e-1;
a := 0.8e-1;
n := 1;

R(r) := BesselJ(n,k r) + B BesselY(n, k r) + C BesselI(n, k r)  + D BesselK(n, k r) ;

eq1 := R(b) = 0;
eq2 := eval(diff(R(x), x), x = b) = 0;
eq3 := eval(diff(R(x), x, x), x = a) = 0;
eq4 := eval(diff(R(x), x, x, x), x = a) = 0;

solve([eq1, eq2, eq3, eq4], [k, B, C, D])

What is it, that I am not doing right?

Thank you very very much for the help in advance!
Andras



daer all

how can i calculate eigenvalue and eigenvectors for a big Matrix?

example Matrix 12*12.

 

thank you

I have the following characteristic equation by use of maple. How do I find a condition on x, that will return real eigenvalues and complex eigenvalues?

 

 

 

Hi,

  Is there any benchmark of the performance of maple on windows 7 64 bit vs linux, especially in solving generalized eigenvalue problem?

 

Thank you very much

 

 

I calculate eigenvalues and  eigenvectors of a floating-point square matrix M with the command Eigenvectors(M, output = 'list').  How can I estimate errors of my results?

So, newb question here. I've done my best to debug this line of code, but to no avail. For some reason this function is NOT getting solved correcting for the zeros:

cos(L*x) - x*sin(L*x)

 

This is not an extremely complex equation either, so I'm at a loss for why my while loop continues to sit there forever. I've got it set to find N number of zeros, but it'll just keep going forever never finding any zeros. I've tried mixing up the start point, and even changed the range which it's searching for them, but nothing seems to get me any closer. Please help!

 

> restart; with(plots);
> a := 0; b := 1/2; N := 5; w := 1; L := b-a;

Eigenvalue equation
> w := cos(L*x)-sin(L*x)*x;
> plot(w, x = 0 .. 50);

> lam := array(0 .. N+1);

> nn := 0; kk := 5; while nn < N do zz := fsolve(w(x) = 0, x = kk .. kk+1); if type(zz, float) then printf("lam(%d)=%f\n", nn, zz); lam[nn] := zz; nn := nn+1 end if; kk := kk+1 end do

 

Hi

i want to find the eigenvalues of this system of two equations with two unknowns:

2.097*k = .9525000000*k^.35-2.2225*b/k^.65+.2 and

(2.097-2.0955/k^.67)*b = -.2

How i can do this in Maple?

Any help will be appreciated

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