1. BWM21403 Mathematics IV Sem I 2013/2014
Instruction : Do the calculations in 3 decimal places.
First Individual assignment: (submit 3rd meeting) 10%
Q1. Given graph of
f ( x ) = x 3 −10 x +10
beside.
(a) Find the least positive root by using
bisection method with | b −a |=1 .
(b) Find the most positive root of f (x ) by
using Newton-Raphson method. Iterate until
| f ( xi ) |< ε = 0.005 .
y
30
20
10
1
2
3
-3
-2
-1
Second Individual assignment: (submit 4th meeting) 10%
Q1. Solve the system of linear equation by using
2 x1
Doolittle method
−
5 x2
+
+
+
2 x2
x2
− 7 x3
+
x3
-4
3x1
− 3x1
Q2 Find the approximate value for
(a) trapezoidal rule,
∫
x3
4
x
= 2
=
=
1
1
1
dx and n = 10 subintervals by using
x
(b) 1/3 Simpson’s rule.
4
0.25
Group assignment : (submit 5th meeting) ( max 4 person in a group) 20%
Q1. Solve the system of linear equation by using
2 x1 − 5 x 2 +
Gauss Seidel iteration
3x1
− 3x1
Q2 Given f ( x ) = e −x .
(a)
Complete the following table.
x
0
0.25
+
+
0.75
2 x2
x2
x3
− 7 x3
+
x3
= 2
=
=
1
1
1.0
f ( x ) = e −x
(b) Hence, find
(i)
P3 (0.4) by using
Lagrange interpolation (ii) Newton divided-difference method.
(c) If (0.5, 0.607) is added into the data above, find f (0.4) by using Newton divideddifference method.
Q3 Given the first-order initial value problem (IVP)
y ′ + 2 y = xe 3 x , with initial condition y (0) = 0 ;
1 3x
1 3x
1 −2 x
xe −
e +
e . Solve by
5
25
25
Euler’s method with step size h = 0.2 for interval 0 ≤ x ≤ 1 . Find its errors.
Runge-Kutta method with step size h = 0.2 for interval 0 ≤ x ≤ 0.4 . Find its errors.
And given that the exact solution is y ( x) =
(a)
(b)