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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
http://wiki.octave.org/wiki.pl?OrthogonalCollocation
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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