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.

Formula

Derivation

Convergence

Consistency

Stability

Suppose one has an equation of the following form:

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

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

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

First (Lax) step:

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

Second step:

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

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

References

• P.D Lax (1960). "Systems of conservation laws". Commun. Pure Appl Math. 13 (2): 217–237. doi: 10.1002/cpa.3160130205. {{ cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) ( help)
• Michael J. Thompson, An Introduction to Astrophysical Fluid Dynamics, Imperial College Press, London, 2006.