# Computational Science

#### Taught by Mike Davis, SGI, Hal Meyer, SGI, and Dick Morse, UNM

Topics: modeling, brute force, given an equation-find the root(s), numerical integration, heat/fluid flow.

modeling
How do you model with computers?

brute force
Exhaustive searching, loops.
Example: Find all combinations of a pennies, nickels, dimes, quarters, and half dollars that total up to \$1.00.
Example 2: If the letter a was worth 1 point, b 2 points, ... z 26 points, find several words that are worth 50 and 100 points.

given an equation-find the root(s)
1. Newton's Method
2. Solving sets of linear equations, Gaussian elimination.
3. Runge-Kutta for Ordinary Differential Equations

Example: solve f(x)=x^5-5x^4+13x^2-7x+8
or
simultaneous equations

numerical integration
1. Simpson's 1/3 Rule for even panels
2. Simpson's 3/8 Rule for odd panels
3. Newton Raphson method.

Example:

heat/fluid flow
Given a cube (three dimensional array), discuss how heat/fluid might flow from one section to another. For accuracy, sections need to be small and that's were a supercomputer is required. Discuss possible formulas for substances and how those are applied to each cell.
Example:

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