IGNOU BCSL-58
- Computer Oriented Numerical Techniques Lab,
Latest Solved Assignment
(July 2024 - January 2025)

Q1. Write a program in C that accepts a decimal number and displays its floating-point equivalent number. You may make assumptions to simplify the program, however, your representation of floating point number should be closer to IEEE 754 standard 32 bit representation.

Q2. Write a program in C to implement Gauss Seidel method for finding the roots of linear equations.

Q3. Write a program in C to implement Bisection method for finding a positive root of the equation X2- 9x + 21 =0. You have to make suitable choice for the bounds.

Q4. Write a program in C for the demonstration of Newton's Backward Interpolation Formula.

Q5. Write program in C for the demonstration of Bessel's Formula.

Q6. Write a program in C to demonstrate the Newton's Divided Difference Method.

Q7. Write a program in C to find the approximate value of the following definite integral using Simpson's 1/3 rule:

Q1. Write a C/C++ program that implements (Do not use pivot condensation) Gaussian elimination method for solving n linear equations in n variables, that calls procedures

(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:
2x + y + z = 7
3x + 2y + 3z = 16
4x + 5y + 3z = 23

Q2. Write a program in C/C++ to find the root of the following equation by using “Bisection Method”.
Equation: 𝑥3 − 5𝑥 + 1 = 0; 𝑥 ∈ [1, 2]

Q3. Write a C/C++ program that approximates a root of the equation f(x) = 0 in an interval [a, b] using Newton-Raphson method. The necessary assumptions for application of this method should be explicitly mentioned. Use the method to find one root of the equation: x3 + 4x2- 19=0.

Q4. Write a C/C++ program that approximates the value of a definite integral using Trapezoidal Rule, with M sample points. Find an approximate value of the integral of 4x2 using the program with 6 intervals over the interval [0, 3].

Q5. Write a C/C++ program that approximates the solution of the initial value problem: y’ = f(t, y) with y(a) = y0 over [a, b] using Euler’s method. Using the program approximate the solution of the initial value problem: y’ = -2ty2 with y(0) =1

Q6. Write a program in C/C++ to calculate the value of “cos x” by using the series expansion given below:

Note:
• Evaluate cos x only upto first three terms.
• Also find the value of cos x by using the inbuilt function.
• Compare the results i.e., the result produced by your program and
• that produced by inbuilt function. Based on comparison, determine error.

Q7. Write a program in C/C++ to find the value of Sin(π/6) by using Lagrange’s Interpolation, the related data is given below

Q8. Write a program that approximates the value of a definite integral using Simpson 1/3 Rule, with M sample points. Find an approximate value of the integral of 2x3/2 using the program with 8 intervals over the interval [1, 9].