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CE50P-2 Week 4
Laboratory Activity
Solution of Non-Linear Equations
ACTIVITIES: Solve the given equations using the indicated numerical method. Use a tolerance level of
0.001%, that is, terminate the algorithm if |𝑒𝑎 | < 0.001% (note: 𝑒𝑎 is absolute approximate error).
1. Use the bisection method to find the root of the function 𝑓(𝑥) = 𝑥 3 − 𝑥 − 2.
a. Show an appropriate graph.
b.
Iteration
1
2
3
4
…
𝑥𝑙
𝑥𝑢
𝑥𝑚
𝑓(𝑥𝑙 )
𝑓(𝑥𝑚 )
𝑓(𝑥𝑙 )(𝑥𝑚 )
|𝑒𝑎 |
𝑓(𝑥𝑢 )
𝑓(𝑥𝑙 )(𝑥𝑚 )
|𝑒𝑎 |
2. Use the bisection method to solve the equation 𝑥 + cos 𝑥 = 0.
a. Show an appropriate graph.
b.
Iteration
1
2
3
4
…
𝑥𝑙
𝑥𝑢
𝑥𝑚
𝑓(𝑥𝑙 )
3. Use the Regula Falsi method to find the solutions to the equation 𝑒 −2𝑥 + 4𝑥 2 − 36 = 0.
(two possible solutions)
a. Show an appropriate graph.
b.
Iteration
1
2
3
4
…
𝑥𝑙
𝑥𝑢
𝑓(𝑥𝑙 )
𝑓(𝑥𝑢 )
𝑓(𝑥𝑟 )
𝑥𝑟
𝑓(𝑥𝑙 )(𝑥𝑟 )
|𝑒𝑎 |
4. Find all solutions of e2x = x + 6, correct to 4 decimal places using the Newton Method.
5. Use the Fixed-Point Iteration Method to find the solutions to the equation sin 𝑥 − 𝑒 −𝑥 = 0 in the
interval (0,1).
a. Show an appropriate graph.
b. Iteration formula: 𝑔(𝑥) =? ? ?
c. Computations
Iteration
1
2
3
4
…
𝑥𝑘
𝑥𝑘+1
|𝑒𝑎 |
SUMMARY: Provide a summary (in your own words) of the process involved in each method you
used in this activity.
CONCLUSION: