1. Numerical Methods Adam Keaney 56446990 Aisling Butler 56625665 Jody Monahan 56544631

2. Numerical Solvers in Engineering Differential equations describe almost everything in the world. Physics Chemistry Engineering Ecology Weather

3. Classic Parachute Example Drag and velocity relationship.[1]

4. More Examples Misalignment error in G.P.S. [2] Car crash computer modelling. [3]

5. Results of ODE Elapsed time is 1.482735 seconds.

6. Graph that shows the difference in the exact analytical solution versus Euler’s solution with and without friction.

7. Our Innovation

8. We created a game. Aim: Fire the projectile out of box and land in designated area. Method: Guess speed and angle of the projectile.

9. Problems Encountered Ball would penetrate past boundary before bouncing off. To counteract this we halved the step-size when it came close to the boundary

10. Problems Encountered Our code, when executed was not particularly efficient. If given more time we could implement the Runge-Kutta method or the Adams-Bashforth method to improve efficiency.

11. Worms

12. Response to Article Disagree with the article  Quality and quantity  Overseas expansion is seen as a positive step for businesses  Second level education not to blame [4]

13. Response to Article Methods of improvement  A Week Of Wonder [5]  Search for problem internally rather than blaming external factors

14. References http://online.redwoods.cc.ca.us/instruct/darnold/ DEProj/sp04/coleron/paper1.pdf [1] http://online.redwoods.cc.ca.us/instruct/darnold/ DEProj/sp04/coleron/paper1.pdf [1 http://ieeexplore.ieee.org/stamp/stamp.jsp?arnu mber=01331391[2] http://ieeexplore.ieee.org/stamp/stamp.jsp?arnu mber=01331391[2 http://www.deskeng.com/articles/aaahdn.htm[3] http://www.deskeng.com/articles/aaahdn.htm[3 http://extranet.hea.ie/index.cfm/page/news/categ ory/134/section/details/id/154 [4] http://extranet.hea.ie/index.cfm/page/news/categ ory/134/section/details/id/154 [4 www.weekofwonder.ie [5] www.weekofwonder.ie