Question 1

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.

Accepted Answer

Floating-point numbers are essential in computer-oriented numerical techniques for representing real numbers, including fractional values, with a trade-off between range and precision. The IEEE 754 standard is the most widely adopted technical standard for floating-point computation, ensuring consistency across different computer systems. This standard defines formats for representing floating-point numbers, including the commonly used 32-bit (single-precision) format.

In the IEEE 754 32-bit s

Question 2

Write a program in C to implement Regula-Falsi method.

Accepted Answer

The Regula-Falsi method, also known as the False Position method, is a root-finding algorithm that combines features of the Bisection method and the Secant method. As taught in BCSL-058, it is an iterative numerical technique used to find the root of a continuous function `f(x)` within a given interval `[a, b]` where `f(a)` and `f(b)` have opposite signs, ensuring a root exists.

This method operates by repeatedly narrowing down the interval containing the root. Unlike the Bisection method whic

Question 3

Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.

Accepted Answer

The Gauss Elimination method is a fundamental algorithm used to solve systems of linear algebraic equations. It transforms the system into an equivalent upper triangular form, which can then be solved efficiently using back substitution. This method is extensively covered in courses like BCSL-058 due to its direct application in numerical techniques.

**Algorithm Overview**

The Gauss Elimination process typically involves two main phases: forward elimination and back substitution. In forward

Question 4

Write a program in C for the demonstration of Stirling's Formula for Interpolation.

Accepted Answer

Stirling's Interpolation Formula is a central difference interpolation technique used to estimate values within a data set, particularly when the interpolation point lies near the middle of the tabulated data. It requires the independent variable (x-values) to be equally spaced. The formula averages terms from Newton's Forward and Backward interpolation formulas, providing a more accurate estimation when interpolating centrally.

From the BCSL-058 course material, we understand that interpolatio

Question 5

Write a C Program for solving the following system of equations using Jacobi method:  5 -1 -1 -1] [X1] = [-4] -1 10 -1 -1 [X2] = [12] -1 -1 5 -1 [X3] = [8] [-1 -1 -1 10] [X4] = [-34] Starting with x(0) = (0, 0, 0, 0). The exact solution is x = (1, 2, 3,4) T.

Accepted Answer

The Jacobi method is an iterative numerical technique used to solve a system of linear equations of the form AX = B. It works by transforming each equation to express one variable in terms of the others. In each iteration, it updates the value of a variable using the values of other variables from the *previous* iteration. This process is repeated until the values of the variables converge to a stable solution within a specified tolerance or after a maximum number of iterations.

The system of e

Question 6

Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²).

Accepted Answer

The Improved Tangent Method, also known as the Modified Euler Method or Midpoint Method, is a numerical technique for solving Initial Value Problems (IVPs) of the form y' = f(t, y) with an initial condition y(t₀) = y₀. It is a second-order Runge-Kutta method, providing a local truncation error of O(h³) and a global error of O(h²), which makes it more accurate than the basic Euler's method.

In BCSL-058, Unit 3, 'Numerical Methods for Ordinary Differential Equations', elaborates on various method

Question 7

Write a program in C to find the approximate value of the following definite integral using Trapezoidal rule and obtain a bound for the error. The exact value of I = ln2 = 0.693147 correct to six decimal places.:  ∫(from 0 to 1) 1/(1+x) dx

Accepted Answer

The Trapezoidal rule is a numerical integration technique used to approximate the definite integral of a function. It works by dividing the area under the curve into a series of trapezoids and summing their areas. This method is fundamental in numerical analysis, especially when an analytical solution for an integral is complex or impossible to find.

For an integral ∫(from a to b) f(x) dx, the Trapezoidal Rule formula with 'n' subintervals is given by: I ≈ (h/2) * [f(a) + 2Σ(from i=1 to n-1) f(

Question 8

Write a program in C to solve the equation x²y' = 1-xy-x²y², y(1) =-1 from x=1 to x=2 by using Taylor series method of O(h²) with h= 1/3 and ¼ and find the actual error at x=2 if the exact solution is y=-1/x.

Accepted Answer

The Taylor series method is a fundamental numerical technique used to approximate solutions to ordinary differential equations (ODEs) with a given initial condition. This method extends the concept of a Taylor series expansion to estimate the value of `y` at a subsequent point `xᵢ₊₁` based on its value and derivatives at `xᵢ`.

For an order O(h²) approximation, we use the first three terms of the Taylor series expansion. Given an initial value problem `y' = f(x, y)` with `y(x₀) = y₀`, the formul

BCSL-058 Solved Assignment — January 2026 / July 2025

Computer oriented Numerical techniques Lab | IGNOU Bachelor of Computer Applications (BCA)

BCSL-058—January 2026 / July 2025

Computer oriented Numerical techniques Lab

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BCSL-058 Assignment Questions — January 2026

QQ1. 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.

QQ2. Write a program in C to implement Regula-Falsi method.

QQ3. Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.

QQ4. Write a program in C for the demonstration of Stirling's Formula for Interpolation.

QQ5. Write a C Program for solving the following system of equations using Jacobi method: 5 -1 -1 -1] [X1] = [-4] -1 10 -1 -1 [X2] = [12] -1 -1 5 -1 [X3] = [8] [-1 -1 -1 10] [X4] = [-34] Starting with x(0) = (0, 0, 0, 0). The exact solution is x = (1, 2, 3,4) T.

QQ6. Write a C program to solve the IVP y' = -ty², y(2) = 1 and find y(2.1) and y(2.2) with h = 0.1 using improved tangent method (modified Euler method) of O(h²).

QQ7. Write a program in C to find the approximate value of the following definite integral using Trapezoidal rule and obtain a bound for the error. The exact value of I = ln2 = 0.693147 correct to six decimal places.: ∫(from 0 to 1) 1/(1+x) dx

QQ8. Write a program in C to solve the equation x²y' = 1-xy-x²y², y(1) =-1 from x=1 to x=2 by using Taylor series method of O(h²) with h= 1/3 and ¼ and find the actual error at x=2 if the exact solution is y=-1/x.