Duplico

This is a Wikipedia user page.
This is not an encyclopedia article or the talk page for an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a mirror site. Be aware that the page may be outdated and that the user whom this page is about may have no personal affiliation with any site other than Wikipedia. The original page is located at https://en.wikipedia.org/wiki/User:Duplico.

Me edit

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 edit

Some articles I want to edit:

Lax-Wendroff method edit

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 edit

Derivation edit

Convergence edit

Consistency edit

Stability edit

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, 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:

{\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.

References edit

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.