IGNOU MPH 14 SOLVED ASSIGNMENT

MPH 14 2025 - English

Tutor Marked Assignment

COMPUTATIONAL PHYSICS

Course Code: MPH-014

Assignment Code: MPH-014/TMA/2024-25

Max. Marks: 50

Note: Attempt all questions. The marks for each question are indicated against it.

1. a) Define true error and relative true error.

b) The approximate value of the derivative of a function f(x)at x can be calculated using the

formula: 

Calculate  for  and (ii) h = 0.05.

Determine the true error and relative true error in each case. 

2. a) Use the bisection method in the interval [2,4] to calculate the root/s of the equation

 up to three iterations. Calculate the absolute relative approximate error at each stage.

b) What are the advantages and drawbacks of the bisection method?

c) In what way is the Newton-Raphson method more beneficial than the bisection method?

3. a) Given the following data for the velocity as a function of time, calculate the velocity at t = 12 s using second order polynomial interpolation in the Newton divided difference method:

b) Explain why one should not use higher order polynomial interpolation. What would be a preferable method of using information from several data points for interpolation?

4. a) Using the trapezoidal rule, estimate the value of the integral   exp( x)dx and the true error.

b) Use Euler’s method for the differential equation  with the initial condition y(0) = 2 to calculate y(2) . Take a value of step size h = 0.5 .

5. a) Determine the first eight random numbers generated by using the linear congruential random number generator with a=c=7 and m=10. What is the period of this random number sequence.

b) Use the Gauss elimination method to solve the system of equations:

x₁ - 2x₂ + x₃ = 0 ; 2x₁ + x₂ - 3x₃ = 5 ; 4x₁ -7x₂ + x₃ = -1

MPH 014 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment

COMPUTATIONAL PHYSICS

Course Code: MPH-014

Assignment Code: MPH-014/TMA/2026

Max. Marks: 50

Note: Attempt all questions. The marks for each question are indicated against it.

1. a) Explain round-off error and truncation error, with one example of each.

b) The series for e^x can be written as:

Calculate the truncation error when the first four terms of the series are used to evaluate e^1.5.

c) Explain why a polynomial is a useful choice for an interpolating function. 

2. a) Use the Secant method with initial guesses of and to calculate the root/s of the equation up to three iterations. Calculate the absolute relative approximate error at each stage.

b) What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method? 

3. a) A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :

b) Calculate the first derivative of the function  at  using the forward divided difference, backward divided difference and central divided difference methods with a step size of  rad. Also calculate the absolute true error in each case. (5+5)

4. a) Evaluate the integral  using the 2-point Gaussian Quadrature Rule with the following values:

−0.577

b) Derive the Runge-Kutta 2nd Order formula for the differential equation

Use this to determine the value of y at given that , using a step size .

5. a) Using the linear congruential random number generator determine the first five random numbers given that: , , , and . Transform these random numbers to lie between 0 and 1. What would be the maximum possible period of this random number sequence?

b) Use the LU decomposition method to solve the following system of equations: