User:Duplico

Me
Hi. I'm an undergraduate in Computer Science and Mathematics at the University of Tulsa in Tulsa, OK. My interests include Information Security, specifically Cryptography; Algorithms; Music, specifically Trumpet and Harmonica; Optimization; Numerical Analysis; and lunch. My work currently is comprised of Technical Writing and research in passive, signature-based protocol identification.

For some reason, my favorite algorithms are Boyer-Moore and Merkle-Hellman, and the latter is probably my favorite Wikipedia page for some reason. I have recently become enamored with Bloom filters.

Some games, computer or otherwise, that I enjoy include Risk, Monopoly, World of Warcraft, Nexus: The Kingdom of the Winds, Dark Ages, QuizQuiz (RIP), Arcanum: Of Steamworks and Magic Obscura, and Neverwinter Nights: Hordes of the Underdark.

To-Do List
Some articles I want to edit:
 * Public-key cryptography
 * Lax-Wendroff method
 * Merkle-Hellman
 * Finite difference method

Lax-Wendroff method
In numerical analysis, the Lax–Wendroff method is a finite-difference method for approximating the solution to hyperbolic partial differential equations. The method is conditionally convergent, with second-order accuracy in both space and time.

Stability
Suppose one has an equation of the following form:


 * $$ \frac{\partial f(x,t)}{\partial t}=\frac{\partial g(f(x,t))}{\partial x}\,$$

where x and t are independent variables, and the initial state, &fnof;(x, 0) is given.

The first step in the Lax–Wendroff method calculates values for &fnof;(x, t) at half time steps, tn + 1/2 and half grid points, xi + 1/2. In the second step values at tn + 1 are calculated using the data for tn and tn + 1/2.

First (Lax) step:


 * $$ \cfrac{f_{i+1/2}^{n+1/2} - \cfrac{f_i^n+f_{i+1}^n}{2}}{(1/2) * \Delta t}=\cfrac{g_{i+1}^n - g_i^n}{\Delta x}.\,$$

Second step:


 * $$ \cfrac{f_i^{n+1} - f_i^n}{\Delta t}=\cfrac{g_{i+1/2}^{n+1/2} - g_{i-1/2}^{n+1/2}}{\Delta x}.\, $$

This method can be further applied to some systems of partial differential equations.