Indian Institute of Technology Kharagpur
Department of Mathematics
MA39110-Advanced Numerical Techniques Lab
End Sem Exam * Date: 16.04.2022 * Mode: Online
Spring 2022
Time-duration: 30 minutes
Total Marks = 40
Instructions:
• Complete the codes in each question by editing the MATLAB codes provided to you in
the zipped folder.
• Do not alter the rest of the codes, only write your line of codes in the blank space provided
after every question, written as a comment.
• Marks will be deducted if the code fails to run and shows any kind of unacceptable error.
Try to use MATLAB versions R2016b and above.
• While submitting, rename the zipped folder as Rollno ANTLAB.
• Write your name and roll number on the top of all 3 MATLAB Codes.
• Your video shall be ON and audio shall be OFF. Failure of this will lead to cancellation
of your exam.
• Only MOODLE SUBMISSION is allowed – link will be open between 10:15 and 10:40 am.
The submission time will not be extended under any circumstances.
• 5 marks will be deducted if not submitted by 10:40 am.
• No outputs are required for any question. Only code has to be submitted.
1. Solve the non-linear boundary value problem using Newton-Raphson method with the
help of a MATLAB code.
y ′′ − 3y − 10y 3 = x2 ,
y(0) = 0
y(1) = 0
with step size h = 0.5. Find the following 4 questions in the MATLAB Code named Q1:
(a) Write a command here to call the NRM function and store its value in the variable
y1 val.
(b) Write a three line code here for Newton Raphson Method.
(c) Calculate error here and save it to err variable.
(d) Write a print statement to display the number of iterations executed.
[12 marks]
1
2. Solve the following linear boundary value problem using spline interpolation method with
the help of a MATLAB code:
y ′′ + Ay ′ + By = C,
y(0) = α, y(1) = β,
where A = −2, B = 1, C = 1, α = 2 and β = e + 1 with the step size h = 0.1. Find the
following question in the MATLAB code named Q2:
(a) Write the equations for k = n − 1.
[12 marks]
3. Consider a thin metal wire of length two meters with no heat exchange with its surroundings such that the heat conductivity of wire is 0.3. Initially the wire is heated with a
temperature distribution x2 (L2 − x2 ) at time t = 0 while both ends of the wire are kept at
a fixed temperature of 0 c for all times t. Then solve the one-dimensional heat equation
to obtain the temperature distribution at a later time t using Crank Nicolson method by
solving a triadiagonal system of linear equations with the help of a MATLAB code. Find
the following 4 questions in the MATLAB code named Q3:
(a) Write down a three line code for entering initial temperature distribution.
(b) Write down a three line code which includes a time loop and call the function
Tridiag(r, RHS) (See at the end of code) to write the Crank Nicolson iteration scheme.
(c) Write down a small code to plot u vs x at specific time points t = 100, 300, 500, 1500.
(d) Write down a small code using a for loop (Back substitution loop) for returning the
value of u to the function Tridiag.
[16 marks]
2