Struct OrthogonalCollocation 

pub struct OrthogonalCollocation;

Orthogonal collocation at Gauss-Legendre points.

Approximates y(t) as a piecewise polynomial, enforcing the ODE at collocation points within each subinterval and matching state values at mesh nodes.

For each subinterval [t_i, t_{i+1}] with m collocation points τ_j:

• The polynomial p(t) satisfies p(t_i) = y_i (left endpoint)
• p’(τ_j) = f(τ_j, p(τ_j)) for j = 1..m (collocation conditions)
• y_{i+1} = p(t_{i+1}) (right endpoint value)

This results in a large nonlinear system that is solved by Newton iterations.

Implementations

impl OrthogonalCollocation

pub fn solve<ODE, BC, Guess>( ode: &ODE, bc: &BC, t_span: [f64; 2], y_init_guess: &Guess, n_state: usize, cfg: &CollocationConfig, ) -> IntegrateResult<BVPResult>

where ODE: Fn(f64, &Array1<f64>) -> Array1<f64>, BC: Fn(&Array1<f64>, &Array1<f64>) -> Array1<f64>, Guess: Fn(f64) -> Array1<f64>,

Solve BVP by collocation at Gauss-Legendre points.

Arguments

• ode - ODE function f(t, y)
• bc - Boundary condition: g(y(a), y(b)) = 0 (n_bc equations)
• t_span - [a, b]
• y_init_guess - Closure providing initial guess for y at time t
• cfg - Collocation configuration