**Course Code : BCSL-058**

**Course Title : Computer oriented Numerical techniques**

**Lab**

**Assignment Number : BCA(5)/L-058/Assignment/2018-19**

**Maximum Marks : 50**

**Weightage : 25%**

**Last Dates for Submission : 15th October, 2018 (For July, 2018 Session)**

**15th April, 2019 (For January, 2019 Session)**

**This assignment has eight problems of 40 marks, each of 5 marks. All problems**

**are compulsory. 10 marks are for viva voce. Please go through the guidelines**

**regarding assignments given in the programme guide for the format of**

**presentation. Note: The programs are to be written in C/C++ and/or in MS-Excel/Any spread**

**sheet.**

Question 1:

Write a program that implements pivot condensation Gaussian

elimination method for solving n linear equations in n variables, that

calls procedure

(i) Exchange of rows

(ii) lower-triangularisation and

(iii) back substitutions

(codes of procedures are also to be written).

Use the program for solving the following system of linear equations:

x + y + z = 3

2x + y+ 3z= 6

4x+5y+2z =11

(5 Marks)

Question 2:

Write a program that uses Gauss-Jacobi iterative method to solve

system of linear equations. Use the method to solve the system of linear

equations given in Q. No. 1 above.

(5 Marks)

Question 3:

Write a program that approximates a root of the equation f (x) = 0 in an

interval [a, b] using Bisection method. The necessary assumptions for

application of this method should be explicitly mentioned. Use the

method to find smallest positive root of the equation

x

4 + 2×3

– 5×2 + 10x – 19=0.

(5 Marks)

Question 4:

Write a program that uses Lagrangian polynomials for interpolation.

You must use only three nodes such that the interpolating polynomial is

at most quadratic. Using this program find approximate value of

f (x) = 2x at x =0.5.

(5 Marks)

17

The nodes are at points x 0 = 0, x 1 = 1, x 2 = 2.

Question 5:

Write a program to interpolate using Newton’s Forward difference

formula having only three points. Solve Problem No. 4 using Newton’s

Interpolating polynomial using Forward difference (instead of

Lagrangian Polynomial).

(5 Marks)

Question 6:

Write a program that approximates the derivative of a given

(differentiable) function f (x) at x = x0, using forward difference formula

taking only 3 points having value of x as 0, 1 and 2 respectively. Using

the program find the derivative of function f(x)=( x )

1/2 at x=0.5

(5 Marks)

Question 7:

Write a program that approximates the value of a definite integral

( )

b

z

f x dx

using Trapezoidal Rule, with M sample points. Find an

approximate value of the integral of 2x

2

using the program with 8

intervals over the interval [0, 4].

(5 Marks)

Question 8:

Write a program that approximates the solution of the initial value

problem:

y f t y

( , )

with

0

y a y ( )

over

[ , ] a b

using Euler’s method.

Using the program approximate the solution of the initial value problem:

y

1 = -2ty2

with y(0) =1

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