ad

Numerical Computing past paper

Numerical Computing all previous/ past question papers

– Numerical Computing-Computer Science all subject past paper Numerical Computing –Computer Graphics  Course  Numerical Computing Project idea – ICT  MCQ -Numerical Computing Interview Question  –Computer Science all courses -Technology –University Past Paper -Programming language –Question paperold paper

Numerical Computing Fall 21 past paper




Numerical computing final paper
Numerical computing final paper

Numerical computing final paper

1. Solve the following system using Jacobi method (with 4 digu roues arithmetic, at least). Assume the error tolerance as 0.0001.

15x₁-2X2-6Xj+0x₁ -2x)+12×2-4X3-X4=300

0 -6×1-4×2+19×3-9×4 =0

0x1-X2-9X3+21x₁=0

(Marks 10)

2. Obtain the first and second derivative at x-7 using Stirling formula. Where

Xp= 12

X

5

6

7

8

9

10

f(x)

196

394

686

1090

1624

2306

(Marks-10)

x

3. Use the table in Question no. 2 of values by Newton forward differentiation formula. To compute f (0.25), (0.50), (0.75).

2125 (Marks= 15)

4. Use Question no. lequations, to find X1, X2, X3, and x, values using Gauss

Jordan Elimination Method.

(Marks 10)

5. Compute ff(x) dx based on Trapezoidal rule. 0.6

X

0

0.1

0.2

0.3

0.4

0.5

0.6

f(x)

0

0.0998

0.1987 0.2955 0.38994

0.4794

0.5646

(Marks-05)

Numerical Computing  Mid term paper

Q1:

Find the Error if found then remove that error?

x F(x)
2.5 24.145
2.0 22.043
2.5 20.225
2.5 18.644
2.2 17.262
3.0 16.047




Q2:

Find the approximate value of following integral for step, h = 0.25

Over the interval [3,9] where f(x) = x/x+3.

  1. Composite Bool’s rule
  2. Composite Weddle’s rule

Q3:

Construct the Newton’s Forward difference interpolating polynomial passing through the points (-1,-3), (1, 5), (3, 17), and (5, 21).

paper 2

Q1:

It is suspected that there is an error in one of the values of f(x) in the following table:

X 0 1 2 3 4 5 6 7 8 9 10
f(x) 0 2 20 90 272 605 1332 2450 4160 6642 10100





Construct the differences-table, detect and correct the error.

Q2:




Q3:

The following table represents the time x and the corresponding velocity f(x) of the particle moving with non-uniform velocity.

X 0.0 1.0 1.5 2.0
f(x) 2.5 1.0 4.6 5.3

From this table, using Lagrange’s formula inversely, determine the time when the velocity of the particle becomes 2.75.

 

Numerical Computing Sessional 1 question paper

NC S1

Numerical Computing Sessional 2 question paper

  1. Filling the blanks (Score: 2 5=10)

(1)     Let ξ=g(ξ)∈[a, b] be a fixed point of the real-valued and continuous function g(x). If g(x) has a continuous derivative in some neighborhood of ξ with ________.

Then the sequence (xk) defined by xk+1=g(xk) converges to ξ as k→∞, provided that x0 is sufficiently close to ξ.

(2)     Assume that .Let be distinct real numbers and suppose that are real numbers. Then, there exists a unique Lagrange polynomial such that ____________.

 

(3)     Suppose that a real-valued function g(x) has a fixed point ξ in [a, b]. Then, the corresponding expression can be written as________.

(4)     Given that 4x2-a=0, where a is positive real number. Then, the iteration for solving this equation by the secant method can be expressed as ____________with x0 and x1 being the starting values.

 

(5)     During the process of finding the single solution to the equation f(x) =0 in [a0, b0] with f(a0)f(b0)<0, the first step is to consider the midpoint . If (the given tolerance), then we need to choose the new interval:[a1, b1]=[a0, c0] in the case of _____;or [a1, b1]=[c0, b0] in the case of _____.

  1. Find solution using Bessel’s formula Score= 10
  2. Find Solution using Newton’s Backward Difference formula    Score=10
x f(x)
3.5 34.145
4.0 32.043
4.5 30.225
5.0 28.644
5.5 27.262
6.0 26.047


x = 4.75

Numerical Computing Final question paper

  1. MCQ’s (Marks=10)
    1. How much significant digits in this number 204.020050?
      1. 5
      2. 7
  • 9
  1. 11
  2. In which of the following method, we approximate the curve of solution by the tangent in each interval.
    1. Hermite’s method
    2. Euler’s method
  • Newton’s method
  1. Lagrange’s method

 

  1. When   do   we   apply   Lagrange’s   interpolation?
    1. Evenly spaced
    2. Unevenly spaced
  • Both
  1. None of above
  2. When   Newton’s   backward formula is used?
    1. To interpolate values
    2. To calculate difference
  • To find approximate error
  1. None of above

 

  1. What are the errors in Trapezoidal rule of numerical integration?
    1. E<Y
    2. E>Y
  • E=Y
  1. None of above

 

  1. Consider the initial value problem; give the condition of the absolute stability for the Euler method. (Marks= 10)

 

  1. Suppose that the function values of f(x) are given in the following table.
X -1 1 2
ln X -3 0 4

(Marks= 10)
Find the approximate function value at the point  by the Lagrange’s interpolation polynomial of degree 2.

 

  1. Use the predictor-corrector method to get the approximate solution of the following initial value problem (Marks= 10)

 

            with h = 0.1, 0 < x < 0.5.

 

  1. Consider the function f(x) = cos x−x=0. Approximate a root of f(x) via Newton’s Method. (Marks= 10)

Numerical Computing Final Paper 2022







 

#Numerical Computing #Computer Science all subject past paper  Numerical Computing #Computer Graphics  Course  #Numerical Computing Project idea  #Numerical Computing MCQ  #Numerical Computing  Interview Question  #Computer Science all courses #Technology #University Past Paper #Programming language  #Question paper  #old paper

Scroll to Top