Subject: Numerical Method (SH553) 
Exam 
Regular 

Level 
BE 
Full Marks 
80 
Program 
B. Agri 
Pass mark 
32 
Year/part 
II/II 
Time 
3 hrs 

Ã¼ Candidates are required to give their answer in their
own words as far as practicable.
Ã¼ Attempt All
questions.
Ã¼ The figures in the margin indicate Full marks.
Ã¼ Assume suitable data if necessary.
1.
Discuss the
difference between absolute error and relative error with appropriate examples.
[4]
2.
Write an
algorithm of Secant method for finding a real root of a non linear equation.
[4]
3.
Find a real root
of the equation sinx= correct up to
four decimal places using NR method. What are the limitations of this method?
4.
Apply Gauss Seidal Iterative Method to solve the linear equations
correct to 2 decimal places. [8]
10x+yz=11.19, x+10y+z=28.08,
x+y+10z=35.61
5.
Find the dominant
Eigen value and the corresponding Eigen vector of the given matrix using power
method.
6.
What is the
practical significance of the least square method of curve fitting? Describe
the normal equations to fit a given set of data to a linear equation y=ax+b [2+6]
7.
Using stirling formula find , given;
8.
Estimate the
value of cos(1.74) from the following data: [4]
x 
1.7 
1.74 
1.78 
1.82 
1.86 
Sin(x) 
0.9916 
0.9857 
0.9781 
0.9691 
0.9585 
9.
Evaluate using the three
point Gaussian quadrature formula.
[6]
10.
Solve the
following simultaneous differential equation using RungeKutta
second order method at x=0.1 and 0.2 dy/dx =xz+1; dz/dx=xy with initial conditions y(0)=0, z(0)=1 [6]
11.
Write a program
in any high level language (C/C++/FORTAN) to solve a first order initial value
problem using classical RK4 Method. [6]
12.
Solve the
elliptic equation on the square mesh bounded by The boundary
values are u(x,0)=10, u(x,3)=90, and u(0,y)=70,
u(3,y)=0, 0<y<3
***
Source: Department
of agricultural engineering, Technical support: Paudelpadamprasad
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