Mathematical & Computational Physics
3 terms
Bessel Functions
Mathematical & Computational Physics
Cylindrical Special Functions
A family of canonical special functions J_α(x) and Y_α(x) serving as solutions to Bessel's differential equation.
x² y'' + x y' + (x² - α²) y = 0 ⇒ y(x) = A J_α(x) + B Y_α(x)
Big O Notation
Mathematical & Computational Physics
Algorithmic Asymptotic Complexity
A mathematical notation classifying algorithms according to how their execution time or memory requirements grow as input size N increases.
f(N) = O(g(N)) if |f(N)| ≤ C |g(N)| for N ≥ N₀
Boundary Value Problem
Mathematical & Computational Physics
Differential Equation Condition
A differential equation together with a set of additional constraints, called boundary conditions, specified at the boundaries of the domain.
Dirichlet: y(a)=y_A; Neumann: y'(a)=y'_A; Robin: α y(a) + β y'(a) = γ