Roll your own Euler and RK4, then validate against SciPy.
Build a small ODE integration library from scratch — explicit Euler and classical RK4 — and validate it against scipy.integrate.solve_ivp on problems with known solutions.
Explicit EulerRunge–Kutta 4Local vs global errorValidation against a reference
Objective
Implement euler(f, y0, t) and rk4(f, y0, t) for systems. Validate on y′=−y (exact e^{−t}) and a harmonic oscillator, reporting global error and comparing to solve_ivp.
Acceptance criteria
0/4
Workspace
Deliverables
•euler + rk4 in a module.
•An error-vs-step-size study.
•A validation plot against solve_ivp.
Stretch goals
•Add an adaptive step (RK45-style) and compare step counts.
•Show energy drift of Euler vs RK4 on the oscillator.