Comments (1)
Will have to think how best to structure this in the code
In the mean time, maybe using CHebyshevDirichletSpace will make the operator banded
Sent from my iPhone
On 11 Nov 2014, at 10:13 am, Richard Mikael Slevinsky [email protected] wrote:
Hi Sheehan,
I'm trying to create the Volterra integral operator and am running into difficulties. Since Integral(d) is an indefinite antiderivative and the Volterra integral operator is from -1...x, it ends up being a banded operator with a boundary row and may need an algebra BandedOperator + Functional....
For instance, suppose we want to solve \int_{-1}^x u(y) dy + u(x) = 1, with solution u(x) = e^{-1-x}.
using ApproxFun
x = Fun(identity)
d = domain(x)
f = Fun([1.0],d)
Volt = Integral(d)
L = Volt + Iu = L\f
does not give the correct solution. Instead,k = 20
Lp = full(L[1:k,1:k]) - [(ldirichlet(d)*Volt)[1:k]';zeros(k-1,k)]
u = Fun(Lp[pad(f.coefficients,20)],UltrasphericalSpace{1}(d))
will give the correct solution. I think some kind of algebra is needed to add Functionals and BandedOperators, because now Lp could be represented as an Array{Operator,1} with a Functional and a BandedOperator. However, the addentries! would have to know to shift the row index by 1.—
Reply to this email directly or view it on GitHub.
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