I have a function that will compute the derivative matrix operator that
transforms coefficients of a Chebyshev interpolant on interval [a, b] of
degree n (so n+1 total Chebyshev basis functions T_0, T_1, … T_n) into the
coefficients of a degree n-1 chebyshev interpolant on [a, b] that is the
exact derivative of the first interpolant. Maybe it could help you:
# derivative matrix
function der_matrix(deg::Int, a::Real=-1, b::Real=1)
N = deg
D = zeros(Float64, N, N+1)
for i=1:N, j=1:N+1
if i == 1
if iseven(i + j)
continue
end
D[i, j] = 2*(j-1)/(b-a)
else
if j < i || iseven(i+j)
continue
end
D[i, j] = 4*(j-1)/(b-a)
end
end
D
end
On Thursday, April 2, 2015 at 10:38:48 AM UTC-4, Tamas Papp wrote:
Hi,
>
> Can someone point me to some Julia code that calculates a matrix for the
> derivatives of the Chebyshev polynomials T_j, at given values, ie
>
> d^k T_i(x_j) / dx^k for i=1,..n, j for some and vector x.
>
> The Chebyshev polynomials themselves are very easy to calculate using
> the recurrence relation, but derivatives are not. Alternatively, maybe
> this can be extracted from ApproxFun but I have not found a way.
>
> Best,
>
> Tamas
>
