EP207 NUMERICAL METHODS MID TERM EXAMINATION 2021
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EP207 NUMERICAL METHODS
BEP2033 NUMERICAL ANALYSIS
MID TERM EXAMINATION (SEP – DEC 2021)
Q1(a) Figure Q1(a) shows the graph of 
= 
and the curve 
= 
, which intercepts at the
point 
1 . Compute the value of 
1 based on false position method. Given a stopping criterion when the approximate percent relative error falls below 5%.
Figure Q1(a)
(10 marks)
(b) Figure Q1(b) shows the output response (
0) of a process, that could be described in a
time-domain equation 
0 (
) = 3(1 − 
−0. 5
), where 
is the time in second. Compute the time required (give the answer up to three decimal places) for the process output to reach 6A.B% of maximum output responses. The computation must be made based on Newton-Raphson method, with initial guess of 
= 0 and a stopping criterion of 1%. (The unknown A and B is the last two digits of your student ID. For a given ID 1001953154, the A and B would be 5 and 4 respectively. Therefore, you will be required tofind the time requiredfor the output to reach 65.4% of the maximum output changes.)
Figure Q1(b)
(10 marks)
Q2 Given the following equations.
2
− 
+ 
= 3. 
−
+ 2
+ 4
= −0.346
4
+ 6
− 
= −0.303
(The unknown A, B, and C is the last three digits of your student ID. For example, with a student ID 1001953154, the value of A, B, and C would be 1, 5, and 4 respectively. Therefore thefirst equation could be rewritten as 2
− 
+ 
= 3. 154.)
(a) Compute the value of 
, 
and 
based on Gauss Elimination method.
(7 marks)
(b) Using the same sets of equation given in Q2a above, compute the value of 
, 
and 
based on Gauss Seidel Iteration method up to 4th iterations. Compute the true percent error based on the values obtained during the 4th iteration.
(13 marks)
2022-06-15
BEP2033 NUMERICAL ANALYSIS