I want to be able to approximate a PDE, but my eigenfunction is an Interpolating function. Is there a way I can use an interpolating function as an initial condition in the PDE. For Example:
k = NDEigensystem[Laplacian[y[x], {x}] , y[x], {x, -1, 1}, 1]
(* {{3.40468*10^-14}, {InterpolatingFunction[{{-1., 1.} *)
NDSolve[
{
-Laplacian[u[x, t], {x}]/2 + x^4*u[x, t] == i*D[u[x, t], t],
u[x, 0] == k[2]
}
, u
, {x, -1, 1}
, {t, 1, 2}
]
During evaluation of In[18]:= NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.
NDSolve[{-Laplacian[u[x,t],{x}]/2 +x^4*u[x,t]==I*D[u[x,t],t], u[x,0]== -k[[2,1]]}, u, {x,-1,1}, {t,1,2}]
with yours. $\endgroup$ – Bill Jul 22 at 16:52