Struct EulerLagrangeSolver 

pub struct EulerLagrangeSolver {
    pub a: f64,
    pub b: f64,
    pub ya: f64,
    pub yb: f64,
    pub n_interior: usize,
    pub step_size: f64,
}

Finite-difference Euler-Lagrange solver for 1D problems.

Minimises J[y] = ∫_a^b L(x, y, y’) dx subject to y(a) = ya, y(b) = yb using a gradient-descent iteration on the interior grid nodes.

Fields

a: f64

Left endpoint a.

b: f64

Right endpoint b.

ya: f64

Boundary value y(a).

yb: f64

Boundary value y(b).

n_interior: usize

Number of interior grid points.

step_size: f64

Step size τ for gradient descent.

Implementations

impl EulerLagrangeSolver

pub fn new( a: f64, b: f64, ya: f64, yb: f64, n_interior: usize, step_size: f64, ) -> Self

Create a new solver on [a, b] with n+1 subintervals.

pub fn h(&self) -> f64

Grid spacing h = (b − a) / (n + 1).

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

Linear initial guess interpolating the boundary conditions.

pub fn solve_arc_length(&self, max_iter: usize) -> Vec<f64>

Run max_iter gradient-descent steps minimising the arc-length functional J[y] = ∫ sqrt(1 + y’²) dx (geodesic in the plane).

Returns the interior y-values at convergence.

pub fn arc_length(&self, y_interior: &[f64]) -> f64

Evaluate the discrete arc-length functional on the given interior values.

Trait Implementations

impl Clone for EulerLagrangeSolver

fn clone(&self) -> EulerLagrangeSolver

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for EulerLagrangeSolver

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.