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User:Duplico

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Me

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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

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Some articles I want to edit:

Lax-Wendroff method

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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

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Derivation

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Convergence

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Consistency

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Stability

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Suppose one has an equation of the following form:

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(xt) 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:

Second step:

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

References

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  • 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.