## can Maple find solution to eigenvalue boundary val...

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]]```

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

## How do you suggest to find eigenvalue of matrix ha...

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)

## How to solve this ODE system?...

Here is a code

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/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]))

## Quickly extract eigenvectors ...

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?

## Matrix Procedure Query...

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 :)

## Eigenvalues and Characteristic Polynomial...

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!!

## Calculating eigenvectors ...

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...

## Certain eigenvalue problem ...

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

## Eigenvalues and eigenvectors of matrix...

daer all

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

example Matrix 12*12.

thank you

## Problem with characteristic equation...

Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

## Gerschorin's theorem Linear Algebra...

worksheet/expressions/copypasteMaple

Gerschgorin := proc (A::Matrix) local Delta, m, n, AA, R, C, i, c, eig, P, Plt; Delta := proc (i, j) if i = j then 0 else 1 end if end proc; m, n := LinearAlgebra[Dimension](A); AA := Matrix(m, n, proc (i, j) options operator, arrow; Delta(i, j)*abs(A[i, j]) end proc); R := evalm(`&*`(AA, Vector(m, 1))); C := {seq(('plottools[circle]')([Re(A[i, i]), Im(A[i, i])], R[i], color = violet), i = 1 .. m)}; c := {seq(('plottools[point]')([Re(A[i, i]), Im(A[i, i])], color = blue, symbol = diamond), i = 1 .. m)}; eig := evalf(LinearAlgebra[Eigenvalues](A)); P := {seq(('plottools[point]')([Re(eig[i]), Im(eig[i])], color = red, symbol = box), i = 1 .. m)}; Plt := `union`(`union`(C, c), P); plots[display](eval(Plt), scaling = constrained) end proc

A := Matrix([[5, 8, 4, -3], [8, -9, 7, 5], [0, 4, 4, 2], [5, -5, 9, -9]]); evalf(LinearAlgebra[Eigenvalues](A), 3); Gerschgorin(A)

worksheet/expressions/pasteMathML

F := Matrix([[2, -1/2, -1/3, 0], [0, 6, 1, 0], [1/3, -1/3, 5, 1/3], [-1/2, 1/4, -1/4, 4]]); evalf(LinearAlgebra[Eigenvalues](F)); Gerschgorin(F)

Could you print A & F ?

regards

## How do I find a condition on a characteristic equa...

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?

## how to determine the nature of an equilibrium poin...

If I have the following system of first order diff eq's:

x'(t)=2x(t)+3y(t)

y(t)=-3x(t)-2y(t)

then can I consider the coefficient matrix A=<<2,-3>,<3,-2>> and compute the eigenvalues of A and infer as follows:

if the eigenvalues are of the same sign- eq point is a node

if they are of opposite signs- eq point is a saddle

if they are pure imaginary- eq point is a center

if they are complex conjugates- eq. point is a spiral

I've been given these conditions but my text says for a linear system of the form x'=Ax, the eigenvalues of A can be used to identify the nature of the eq. point. I am confused as to whether this applies to the given system as well; I have obtained 5 different trajectories and drawn the phase diagram for the system

## Performance of maple on Windows vs Linux...

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