Mathematical & Computational Physics

A computational architecture where large physical calculations are divided into smaller sub-tasks executed simultaneously across multiple…

Amdahl's Law Speedup S(P) = 1 / ((1 - p) + p / P) Speedup Factor S(P)

Differential equations containing unknown multivariable functions and their partial derivatives with respect to multiple independent…

Elliptic (Laplace), Parabolic (Heat), Hyperbolic (Wave) Multivariable Differential Equations

Mathematical & Computational Physics

A set of mathematical approximation methods for finding an approximate solution to a complex problem by starting from the exact solution of…

H = H₀ + λ H', E_n = E_n^(0) + λ E_n^(1) + λ² E_n^(2) + ... Approximation Power Series

Mathematical & Computational Physics

The use of computer programs and numerical algorithms to simulate the time-dependent physical behavior of real-world or theoretical systems.

x(t + Δt) = x(t) + v(t) Δt + ½ a(t) Δt² Computational Modeling

Mathematical & Computational Physics

An algebraic operation between two phase space functions describing time evolution and conservation laws in Hamiltonian mechanics.

{f, g} = ∑ ((∂f / ∂q_i)(∂g / ∂p_i) - (∂f / ∂p_i)(∂g / ∂q_i)) Phase Space Operation