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From: Saurabh Mahapatra on 31 Jul 2010 21:05
All the statements I make below can be found in an introductory differential equation book (Pick an old one though).

Typically, C would be computed based on a physical system which will have parameters. (like n bodies connected to each other by springs and the springs are parameters). C will be some combination of these parameters and need not be simple. As you change these parameters, C's behavior (as a function of those parameters) and its eigen values will change. Eigen values (denoting the modes) have influence the dynamics of the overall system and if you think harder, also the numerical solution of the problem.

Hope this helps.

Thanks,

Saurabh
From: qetuol greg on 1 Aug 2010 06:01
"Saurabh Mahapatra" <saurabh.mahapatra(a)mathworks.com> wrote in message <i32h81$i6j$1(a)fred.mathworks.com>...
> All the statements I make below can be found in an introductory differential equation book (Pick an old one though).
>
> Typically, C would be computed based on a physical system which will have parameters. (like n bodies connected to each other by springs and the springs are parameters). C will be some combination of these parameters and need not be simple. As you change these parameters, C's behavior (as a function of those parameters) and its eigen values will change. Eigen values (denoting the modes) have influence the dynamics of the overall system and if you think harder, also the numerical solution of the problem.
>
> Hope this helps.
>
> Thanks,
>
> Saurabh

I need to compute the wave propagation through a transparent periodic medium, which period is under the wavelength of the light, so i need to use Maxwell's equations instead of classical scalar diffraction theory. Matrix C is deduced from the relative permittivity of the medium. C is close to a singular matrix however its not, only 2 of the eigenvalues of C are non-zero, the others are.

I tried to use that ode functions, unfortunately i always got errors. Im not sure how to phrase this command correctly:

solution=ode15i(C,[interval of independent],initial conditions)

^this one doesnt work. Any advice?
From: Yi Cao on 1 Aug 2010 07:58
"qetuol greg" <rerros(a)yahoo.com> wrote in message <i33gl0$lgt$1(a)fred.mathworks.com>...
> "Saurabh Mahapatra" <saurabh.mahapatra(a)mathworks.com> wrote in message <i32h81$i6j$1(a)fred.mathworks.com>...
> > All the statements I make below can be found in an introductory differential equation book (Pick an old one though).
> >
> > Typically, C would be computed based on a physical system which will have parameters. (like n bodies connected to each other by springs and the springs are parameters). C will be some combination of these parameters and need not be simple. As you change these parameters, C's behavior (as a function of those parameters) and its eigen values will change. Eigen values (denoting the modes) have influence the dynamics of the overall system and if you think harder, also the numerical solution of the problem.
> >
> > Hope this helps.
> >
> > Thanks,
> >
> > Saurabh
>
> I need to compute the wave propagation through a transparent periodic medium, which period is under the wavelength of the light, so i need to use Maxwell's equations instead of classical scalar diffraction theory. Matrix C is deduced from the relative permittivity of the medium. C is close to a singular matrix however its not, only 2 of the eigenvalues of C are non-zero, the others are.
>
> I tried to use that ode functions, unfortunately i always got errors. Im not sure how to phrase this command correctly:
>
> solution=ode15i(C,[interval of independent],initial conditions)
>
> ^this one doesnt work. Any advice?

The ODE equation is a second ordr ODE. In order to use Matlab, you have to convert it into a set of 1st order ODE's as shown in the thread you referred. Assume the initial value of y is y0.

n = numel(y0);
A = [zeros(n) C;eye(n) zeros(n)];
x0 = zeros(n,1);
z0 = [y0;x0];
z = ode45(@(t,x)A*x, [0 100], z0);

HTH
Yi
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