Re: How to find the eigenvalues/eigenfunctions of a

*To*: mathgroup at smc.vnet.net*Subject*: [mg113399] Re: How to find the eigenvalues/eigenfunctions of a*From*: Mark McClure <mcmcclur at unca.edu>*Date*: Wed, 27 Oct 2010 05:15:30 -0400 (EDT)

On Tue, Oct 26, 2010 at 5:34 AM, Nasser M. Abbasi <nma at 12000.org> wrote: > Given Lu==u''[x], with boundary conditions u'[0]==0,u'[1]==0, need to > find the eigenvalues and eigenfunctions of L. You could do something like a shooting method, with the parameter lambda as the input to your shooting function. Algebraically, this would look like so: Clear[u, lambda]; sol = DSolve[{u''[x] + (lambda^2) u[x] == 0, u[0] == 1, u'[0] == 0}, u[x], x]; u[x_] = u[x] /. First[sol] Now the question is, for which values of the parameter lambda is u'[1]==0? Reduce[u'[1] == 0, lambda] You can also do it numerically. shot[lambda_?NumericQ] := Module[{u}, u[x_] = u[x] /. First[NDSolve[ {u''[x] + (lambda^2) u[x] == 0, u[0] == 1, u'[0] == 0}, u[x], {x, 0, 1}]]; u'[1]]; FindRoot[shot[lambda] == 0, {lambda, 3}] Once you have an eigenvalue, an eigenfunction is easy to find. Mark McClure Mark McClure