1. Latihan Test
1. Fit a Newton`s divided difference interpolating polynomial to estimate log 8.8 using the data
below;
log 7 = 0.845, log 8 = 0.903 and log 9 = 0.954.
Find the absolute error for this approximation where the exact value can be found from your
calculator.
(10 marks)
2. Given the following initial value problem (IVP) at 1<x<2 and h=0.2,
dy
( x − y) = 4 y 4 + 10 xy with y(1)=1
dx
(a) Determine f ( x, y ) from the above IVP. (2 marks)
(b) Hence, solve by using Euler method. (8 marks)
Answer.
2. 1. Newton divided difference; 1
For log 8.8, given;
log 7 = 0.845, log 8 = 0.903, and log 9 = 0.954
i. Draw table;
1 2
i x f(x) f(x) f(x)
0 7 0.845 A = 0.058 C = -0.004
1 8 0.903 B = 0.051
2 9 0.954
ii. Calculate value of A, B and C;
1
0.903 – 0.845
A= = 0.058
8-7 1
0.954 – 0.903
B= = 0.051
9-8
0.051 – 0.055
C= = -0.004
9-7
iii. Substitute the value in the equation;
0 1 2
Pn(x) = 0f + 0f (x-x )+f (x-x )(x-x )
0 0 0 1
P (x) = 0.845 + 0.058 – 0.004 (x – 7) (x – 8)
2
P 2 8.8) = 0.845 + 0.058 – 0.004 (8.8 – 7) (8.8 – 8)
(
Approximate value of log 8.8 from the equation = 0.944
From calculator; log 8.8 = 0.944
So, in order to find the absolute error,
│exact - approximate│
