Questions
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Qns. By Syllabus

Semester

Subject

Year

Bachelors Level/Second Year/Third Semester/Science bit/third semester/numerical methods/syllabus wise questions

Bachelors In Information Technology

Institute of Science and Technology, TU

Numerical Methods (BIT203)

Year Asked: 2079, syllabus wise question

Interpolation and Regression
1.
What are the applications of interpolation? Differentiate between interpolation and regression. Consider the following data points estimate the f(10)f(10) using Lagrange's interpolation.
x56911y13141516\begin{array}{|c|c|c|c|c|c|}\hline x & 5 & 6 & 9 & 11 \\ \hline y & 13 & 14 & 15 & 16 \\ \hline \end{array}
[10]
2.
What is least squares method of fitting a function? Fit the second order polynomial for the following data values.
x1234567y2678101215\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline y & 2 & 6 & 7 & 8 & 10 & 12 & 15 \\ \hline \end{array}
[5]
Numerical Differentiation and Integration
1.
What do you mean by numerical integration? Write any one application of numerical integration. Write an algorithm and c program to implement multi-segment trapezoidal rule. [10]
2.
Construct the divided difference table for the following data value and find first and second order derivative at x=2.
x124810y0152127\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 4 & 8 & 10 \\ \hline y & 0 & 1 & 5 & 21 & 27 \\ \hline \end{array}
[5]
3.
Why it is better to use composite simpson's 3/8 rule instead of simpson's 3/8 rule? Find the value of integration for following data set using simpson's 3/8 rule.
x0123456y10.50.20.10.05880.03850.027\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & 1 & 0.5 & 0.2 & 0.1 & 0.0588 & 0.0385 & 0.027 \\ \hline \end{array}
[5]
Solution of Nonlinear Equations
1.
Define true error and relative error. Derive the bisection method for solving non-linear equation and using this method solve 2x3−2x−52x^3-2x-5 with initial x0=1x_0=1 and x1=2x_1=2. Calculate upto 10th iteration. [10]
2.
Write an algorithm for Honer's method. Evaluate the polynomial f(x)=x4+3x3+5x2+7x+9f(x) = x^4 + 3x^3 + 5x^2 + 7^x + 9 at x = 2 by using Honer's method. [5]
Solution of Ordinary Differential Equations
1.
Find the approximate value of y when x = 0.6 of dy/dx=1−2xydy/dx = 1-2xy, given that y = 0 when x = 0 with h=0.2 using Heun's method. [5]
Solution of Partial Differential Equations
1.
Consider a steel plate of size 24cm x 24cm. If two of the opposite sides are held at 100 degree Celsius and the other two opposite sides at 0 degree Celsius, find the steady state temperatures of interior points, assuming a grid size of 8cm x 8cm. [5]
Solving System of Linear Equations
1.
Solve the following system of linear equations using Gaussian elimination method. 2x+2y+z=122x+2y+z=12, 3x+2y+2z=83x+2y+2z=8, 5x+10y−8z=105x+10y-8z=10 [5]
2.
Solve the following system of linear equations using Gauss-Seidal method. 10x+y+z=1210x+y+z=12, 2x+10y+z=132x+10y+z=13, 2x+2y+l0z=142x+2y+l0z=14 [5]
3.
Define eigen value and eigen vector. Explain how shooting method is used to solve boundary value problem. [5]