Mathematical & Computational Physics
3 terms
Nonlinear Dynamics
Mathematical & Computational Physics
Phase Space Dynamics
The study of physical systems governed by non-linear equations where output changes are not directly proportional to input changes.
d x / dt = f(x) (where f is non-linear)
Numerical Linear Algebra
Mathematical & Computational Physics
Matrix Factorization Algorithms
The subfield of numerical analysis studying algorithms for performing matrix operations efficiently and accurately on digital computers.
LU: A = L U, QR: A = Q R, SVD: A = U Σ V^T
Numerical Stability
Mathematical & Computational Physics
Algorithm Stability Property
The property of a numerical algorithm ensuring that errors introduced during computation do not magnify uncontrollably over successive time steps.
Von Neumann Stability Analysis: |G(k, Δt)| ≤ 1