## orthovald

Orthogonal (and its derivatives) evaluation.

Orthogonal (and its derivatives) evaluation.

f = orthovald(N, ord, x, domain, basis)

f = orthovald(N, ord, x, domain, basis) returns the value of a polynomial evaluated (orthogonally) at x. The diference betwwen orthovalv and orthovald is that the former returns f in the basis, while the latter returns f along with its derivatives. Relation: sum(orthovald(N, 0, x, ...)) = orthovalv(ones(10, 1), x, ...), if x is a scalar. This function is useful, for instance, to build the C block for the initial/boundary conditions.

N = matrix such that NPa = diff(P) (double matrix). ord = derivative order (integer scalar). x = input for evaluation (double scalar). domain = domain [a b] of orthogonality (double vector). basis = orthogonal polynomial basis (integer scalar or char). 1 or 'ChebyshevT' to Chebyshev of first kind, 2 or 'ChebyshevU' to Chebyshev of second kind, 3 or 'LegendreP' to Legendre, 4 or 'HermiteH' to Hermite, 5 or 'LaguerreL' to Laguerre and 6 or 'GegenbauerC' to Gegenbauer.

f = [P0^(ord)(x), P1^(ord)(x), ...] (double vector).

orthovalv, orthovalvj, orthovalM and orthovalMj.