Brownian Motion
Published:
Brief History
Definition
Examples
Gaussian Orthogonal Ensemble (GOE)
The eigenvalues will always be correlated.
Advection Equation
Approximation methods:
- Leap-Frog: central diff
- Lax-Wendroff: Taylor. Plug in the Advection eqn into the Taylor expansion. u(n + delta t) define then compute u’ and u’’. D_x^2: square the matrix or apply the Dx twice?
Von Neumann Analysis
Fourier basis.
{U_m}^n = e^{im\delta x w} multiply by g(w) Goal: ensure that |g| \leq 1
LW: Plug in the U_m^{n+1} into the Fourier space.
Leapfrog:
Heat Equation:
- Explicit 2-level
- Crank-Nicolson