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Mathematical & Computational Physics

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Mathematical & Computational Physics

Nonlinear 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) Phase Space Dynamics Mathematical & Computational Physics

Numerical Linear Algebra

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 Matrix Factorization Algorithms Mathematical & Computational Physics

Numerical Stability

The property of a numerical algorithm ensuring that errors introduced during computation do not magnify uncontrollably over successive time…

Von Neumann Stability Analysis: |G(k, Δt)| ≤ 1 Algorithm Stability Property