Module ode 

ODE solver primitives (Euler, RK4 step functions). ODE / PDE Solver Infrastructure — Minimal Primitives

These are stub primitives designed for future library integration (Bastion). They provide the foundational stepping functions; full solver loops and adaptive algorithms will be built as CJC library code on top of these.

Enums

SymExpr

Symbolic expression representation for automatic symbolic differentiation.

Functions

adjoint_solve

Adjoint method for Neural ODEs — O(1) memory gradient computation.

ode_solve_rk4

Full RK4 solver: integrates dy/dt = f(t, y) over [t0, t1] using n_steps equal steps.

ode_solve_rk45

Adaptive Dormand-Prince RK45 solver.

ode_step_euler

Single step of Euler’s method: y_{n+1} = y_n + h * f(t_n, y_n).

ode_step_rk4

Single step of classical RK4: 4th-order Runge-Kutta.

pde_laplacian_1d

1D finite-difference Laplacian: d^2u/dx^2 ≈ (u[i-1] - 2*u[i] + u[i+1]) / dx^2

pde_step_diffusion

Single explicit Euler step for a heat/diffusion PDE: u_{n+1} = u_n + dt * alpha * laplacian(u_n)