PHY 314 Pass Questions

NATIONAL OPEN UNVERSITY OF NIGERIA

JABI, ABUJA

FACULTY OF SCIENCE

SEPTEMBER/OCTOBER 2016 EXAMINATION

COURSE CODE: PHY314

COURSE TITLE: NUMERICAL COMPUTATION

TIME: 2 Hours 30 Minutes

INSTRUCTION: Answer any four questions.

1. (a) Solve the system of linear equations

x  y  z  1, x  2y  2z  4, 9x  6y  z  7

using the method of (a) Gaussian elimination

(b) Solve the following system of equations using the method of LU decomposition.

2x  y  z  5

x  3y  2z  5

3x  2y  4z  3

2(a) Find a zero of the function

( ) 2 3 2 3

3 2

f x  x  x  x 

between the points 1.4 and 1.7, using

the bisection method. Take the tolerance to be

5

|

1

| 10

x j  x j  .

3.(a) A student obtained the following data in the laboratory.

t5 12 19 26 33

x23 28 32 38 41

By making use of the method of least squares, find the relationship between x and t.

(b) Solve the problem in 1(a) using the method of group averages and compare the results

obtained by the two methods.

4.(a) Find the zeros of the function

( ) 2 3 2 3

3 2

f x  x  x  x 

using the Newton-Raphson

method, starting with

x= 1.4. Take the tolerance to be

5|

1

| 10

x j  x j  .

(b) Find the root of the equation

( ) 2 3 2 3

3 2

f x  x  x  x 

between x = 1.4 and 1.7 by the

regula-falsi method.

5.(a) Find the wrong entry in the following table, given that they represent a cubic polynomial.

x

0 1 2 3 4 5 6 7 8

y -2 4 34 106 238 448 754 1174 1726

(b) Find the cubic polynomial that fits the following table.

x 1 2 3 4

y 3 9 27 63

6..(a) Carry out the forward, backward, and the central difference schemes on the set of data

provided below:

1 2 3 4 5 6 7

1 12 47 118 237 416 667

(b) Starting with the function

8 8 2 12 3 2

x  x  x  , draw up a difference table.

Deduce the equation that fits the data, starting from the table alone.

7.(a) Integrate the function

2

2

5

2

1

( )

2

x t  t  t  , 0  t  0.6

, with six intervals, using the

Simpson’s one-third rule

(b) With the aid of the Euler method, calculate

y(0.8)

, given the differential equation

x y

dx

dy

 

;

y(0)  0

; with

h  0.2