Struct ImplicitEuler 

pub struct ImplicitEuler {
    pub max_iter: usize,
    pub tol: f64,
    pub fd_eps: f64,
}

Implicit (backward) Euler integrator for stiff ODEs.

Solves the nonlinear system y_{n+1} - y_n - h * f(t_{n+1}, y_{n+1}) = 0 using fixed-point (Picard) iteration followed by Newton correction steps.

Fields

max_iter: usize

Maximum Newton iterations per step.

tol: f64

Convergence tolerance for Newton iteration.

fd_eps: f64

Finite-difference step size for the Jacobian.

Implementations

impl ImplicitEuler

pub fn new(max_iter: usize, tol: f64, fd_eps: f64) -> Self

Construct with specified parameters.

pub fn default_params() -> Self

Construct with default parameters.

pub fn step<F>(&self, s: &OdeState, h: f64, f: &F) -> OdeState

where F: Fn(f64, &[f64]) -> Vec<f64>,

Perform one backward Euler step from state s with step h.

Uses simple fixed-point / Picard iteration (no Jacobian required). For strongly stiff systems prefer Newton iteration via ImplicitEuler::step_newton.

pub fn step_newton<F>(&self, s: &OdeState, h: f64, f: &F) -> OdeState

where F: Fn(f64, &[f64]) -> Vec<f64>,

Perform one backward Euler step using finite-difference Newton iteration.

More robust than fixed-point for stiff problems. Approximates the Jacobian column-by-column with forward differences.

pub fn integrate<F>( &self, s0: &OdeState, t_end: f64, dt: f64, f: &F, ) -> Vec<OdeState>

where F: Fn(f64, &[f64]) -> Vec<f64>,

Integrate from s0 to t_end with fixed step dt.

Uses Newton iteration per step for robust handling of stiff problems.