scipy-numerical

What problem does it solve?

It helps you compute and analyze physics systems numerically when closed-form solutions are unavailable, covering time evolution, spectral content, and parameter optimization.

Core Features & Use Cases

• ODE/IVP solving: Simulate nonlinear dynamics with scipy.integrate.solve_ivp, including method selection for non-stiff vs stiff regimes (e.g., RK45, Radau, BDF).
• PDE discretization: Solve a 1D diffusion/heat equation using sparse finite-difference matrices and time-stepping schemes like Crank–Nicolson.
• Spectral analysis with FFT: Perform FFT-based power spectral density estimation and compare methods such as Welch PSD for noisy signals.
• Optimization & fitting: Fit physically motivated models (e.g., damped cosines) with uncertainty estimation via covariance matrices.
• Sparse linear algebra: Compute eigenvalues/eigenstates for quantum-like operators using sparse eigensolvers (e.g., eigsh).

Quick Start

Use the scipy-numerical skill to simulate a Lorenz attractor with solve_ivp and visualize the 3D trajectory for method RK45.