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Re: boundary value + eigen value problem

From: Geordie McBain
Subject: Re: boundary value + eigen value problem
Date: Fri, 15 Oct 2004 10:10:45 -0400

Once you've discretized the ODE, so that H is a known square matrix, Si
is an unknown column vector (eigenvector), and E is an unknown number
(eigenvalue), you can use the octave function eig, which is described in
the manual under `Linear Algebra/Basic matrix functions', basically, E =
eig (H).

One way to discretize two-point boundary value problems like this is
orthogonal collocation.  For this, use the octave function colloc,
described in `Quadrature/Orthogonal collocation'.

As noted at ScaryOctave

there are some good examples of the use of colloc for 2-pt BVPs in the
book `Chemical Reactor Analysis and Design Fundamentals' by J. B.
Rawlings & J. G. Ekerdt (Nob Hill, 2002).

Hope this helps,

Geordie McBain

On Thu, 2004-10-14 at 03:24, Y U Sasidhar wrote:
> Which octave function can be used to solve equations of type:
> k*Si(x)''+V(x)*Si(x)=E*Si(x)
> with  Si(0)=value1; Si(10)=value2
> Si'' -- second drivative of Si
> ( this is a form of Schrodinger equation H Si = E Si )

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