Struct ChebyshevCollocation 

pub struct ChebyshevCollocation {
    pub n: usize,
}

Chebyshev collocation method for 1D boundary value problems.

Sets up the collocation differentiation matrix on Chebyshev-Gauss-Lobatto nodes and solves second-order BVPs of the form p(x) u'' + q(x) u' + r(x) u = g(x) with Dirichlet boundary conditions.

Fields

n: usize

Number of interior collocation points (polynomial degree = n+1).

Implementations

impl ChebyshevCollocation

pub fn new(n: usize) -> Self

Construct a collocation scheme with n Chebyshev-Gauss-Lobatto points.

pub fn nodes(&self) -> Vec<f64>

Return the collocation nodes (Chebyshev-Gauss-Lobatto on [-1, 1]).

pub fn diff_matrix(&self) -> Vec<Vec<f64>>

Return the first-derivative spectral differentiation matrix D of size n x n.

pub fn solve_poisson<G>(&self, g: G, bc_left: f64, bc_right: f64) -> Vec<f64>

where G: Fn(f64) -> f64,

Solve the 1D Poisson equation u'' = g(x) on [-1, 1] with Dirichlet boundary conditions u(-1) = bc_left, u(1) = bc_right.

Uses the Chebyshev spectral differentiation matrix; applies boundary conditions by replacing the first and last rows. Returns u at all collocation nodes.