Module ode_pde 

ODE and PDE solver kernels.

Provides CPU-side implementations of numerical methods for ordinary and partial differential equations. In production these algorithms would generate PTX kernels for GPU execution; the CPU reference implementations here ensure correctness and serve as the algorithmic specification.

ODE solvers

• Euler — first-order forward Euler
• RK4 — classical fourth-order Runge-Kutta
• RK45 — Dormand-Prince 4(5) with adaptive step-size control
• Implicit Euler — backward Euler for stiff systems (Newton iteration)
• BDF2 — second-order backward differentiation formula

PDE solvers

• Heat equation (1-D) — explicit FTCS and implicit Crank-Nicolson
• Wave equation (1-D) — leapfrog / Störmer-Verlet
• Poisson equation (1-D) — direct tridiagonal solve
• Advection equation (1-D) — first-order upwind and Lax-Wendroff

Structs

AdvectionEquation1D

1-D advection equation solver: du/dt + a * du/dx = 0.

Bdf2Solver

Second-order backward differentiation formula (BDF2) solver.

EulerSolver

Forward Euler solver.

Grid1D

One-dimensional uniform grid.

Grid2D

Two-dimensional uniform grid.

HeatEquation1D

1-D heat equation solver: du/dt = alpha * d²u/dx².

ImplicitEulerSolver

Backward (implicit) Euler solver — suitable for stiff systems.

OdeConfig

Configuration for an ODE integration.

OdeSolution

Solution returned by an ODE solver.

PdeConfig

Configuration for a 1-D PDE solve.

Poisson1D

1-D Poisson equation solver: -u’’ = f, with boundary conditions.

Rk4Solver

Classical fourth-order Runge-Kutta solver.

Rk45Solver

Dormand-Prince 4(5) adaptive solver (RK45).

StepResult

Result of a single integration step (adaptive methods).

WaveEquation1D

1-D wave equation solver: d²u/dt² = c² * d²u/dx².

Enums

BoundaryCondition

Boundary condition type.

OdeMethod

Integration method selector.

Traits

OdeSystem

Right-hand side of an ODE system dy/dt = f(t, y).

Functions

numerical_jacobian

Compute the numerical Jacobian of an ODE system by finite differences.

solve_tridiagonal

Solve a tridiagonal system using the Thomas algorithm.