18 September 2007

KKKQ 3013KKKQ 3013PENGIRAAN BERANGKAPENGIRAAN BERANGKA

Week 11 – Ordinary Differential Equations18 September 2007

8.00 am – 9.00 am

18 September 2007 Week 11 Page 2

Topics

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Tutorial Example 1 (adapted courtesy of ref. [1])

Solve the following initial value problem for t = 2.0, given y(0) = 2.

Use the 4th order Adams method. Employ a step size of 0.5. [ Exact solution: y = 2 / (1 + t)2 ]

[1] Chapra, S.C & Canale, R.P, Numerical Methods for Engineers, McGraw-Hill 5th ed. (2006)

t

y

dt

dy

1

2

Apply the 4th order Runge Kutta method to predict the start-up values.

18 September 2007 Week 11 Page 4

Tutorial Example 1 (adapted courtesy of ref. [1])

18 September 2007 Week 11 Page 5

Tutorial Example 1 (adapted courtesy of ref. [1])

18 September 2007 Week 11 Page 6

Tutorial Example 1 (adapted courtesy of ref. [1])