ffsshhttiikk What I do
- Implement numerical integration methods (Runge-Kutta, Verlet)
- Solve partial differential equations (finite difference, FEM)
- Monte Carlo simulations for statistical systems
- Implement spectral methods (FFT-based solutions)
- Optimize computational performance for physics problems
- Validate simulations against analytical solutions
When to use me
When analytical solutions are intractable and numerical simulation is needed for physical systems.
Key Concepts
- Finite Difference: Approximate derivatives as (f(x+h) - f(x))/h
- Runge-Kutta 4th Order: y_{n+1} = y_n + (k₁ + 2k₂ + 2k₃ + k₄)/6 with staged evaluations
- Verlet Integration: Symplectic method preserving energy for molecular dynamics
- Fast Fourier Transform: O(N log N) for solving PDEs in spectral space
- Monte Carlo: Random sampling for integration in high dimensions
- Finite Element Method: Mesh-based solution for complex geometries