IGNOU BCSL-58
- Computer Oriented Numerical Techniques Lab,
Latest Solved Assignment
(July 2023 - January 2024)

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].

Q1. Write a program in C/C++ to find the solution of system of linear equations (given below), by using Gauss- Elimination method:
𝑥 + 𝑦 + 𝑧 = 2
𝑥 − 2𝑦 + 3𝑧 = 14
𝑥 + 3𝑦 − 6𝑧 = −23

Q2. Write a program in C/C++ to determine the approximate value of the definite integral (I) (given below), by using Simpson’s (1/3)rd rule:

Using step size (ℎ) = 0.2 .

Q3. Write a program in C or C++ to demonstrate the following operations, for the function 𝑓(𝑥) = 𝑥2 + 𝑥 + 7 ∶
(a) Forward Difference Operator
(b) Central Difference Operator

Q4. 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:

Q5. 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.