BharatiyaVidya Bhavan's
SARDAR PATEL COLLEGE OF ENGINEERING, MUMBAI
DEPARTMENT OF MECHANICAL ENGINEERING
T1- TERM EXAMINATION, MARCH 2023
PROGRAM: TY B.Tech. (Mechanical), Semester-VI
COURSE: OE-BTM611 - Computational Methods
Total points: 20
Duration: 1 HOUR
Note:
Answer ALL questions.
Answer should be question specific and to the point.
Allcomponent of a question must be answered together.
Data in the last column represents Course Outcome and Blooms Taxonomy of
respective question
COBT
Q1. What is mathematical modelling? 10 1,2/1,3
Consider a light emitting electric glass bulb. The filament of the bulb is
heated by passing electric current through it. The filament temperature rises
and it starts glowing. It is surrounded by inert gases and covered by a glass
bulb. Over a period of working, the temperature of gas and the glass bulb
increases. Develop mathematical model to estimate
i) the transient variation of gas temperature
ii) the transient variation of glass temperature
Write allassumptions you made to develop the model.
Q2. A. Write four basic difference between analytical solution and numerical 4 1,2/2,3
solution.
B. Differentiate between with illustrations 6
i) Accuracy and precision
i) True error and approximate error
iii) Round off error and Truncation error
Bharatiya Vidya Bhavan's
SARDAR PATEL COLLEGE OF ENGINEERING, MUMBAI
DEPARTMENT OF MECHANICAL ENGINEERING
T2- TERM EXAMINATION, APRIL 2023
PROGRAM: TY B.Tech (C/M/E)., Semester-VI
COURSE: OE-BTM611 COMPUTATIONAL METHODS
Total points: 20
Duration: 1 HOURS
Note:
Answer ALL questions.
Answer should be question specific and to the point.
" Allcomponent of a question must be answered together.
Data in the last column represents Course Outcome and
Blooms Taxonomy of respective question
CO/BT
Q1. (A) Acoefficient mentrix is decomposed into Land U matrix as shown 3 1,3/3
below. Use the techniques of LU decomposition to calculate the vales of
variables.
1 0 05 4 3 Tx. 1
|0.4 1 0l0 -0.6 -3.2|| X =7
|0.6 0.67 1||0 0 2.33 || X,|12|
(B) What you understand by the following terms (Answer any four). Explain 8 1,2/2
them also.
1. Truncation errors in computation
2. Diagonal dominance
3. Relaxation factors
4. Convergence limits
5. Condition number
Q2. (A)Solve the following set of equations by the Gauss -Seidel method without 5 3/4
relaxation. Show the formulation for iterative solution and result in the
tabular form for initial five (5) iterations.
4 -1 1 X127
-1 4 -2||x, =-1
|1 -2 4| X 5
(B) Use Secant Method to find the root of equation: x-6x*+8x +0.8=0 4 3/4
Start with initial guess of x1=2.5 and x =2.0. Show result up to next 3
iterations.
Bharatiya Vidya Bhavan's
SARDAR PATEL COLLEGEOF ENGINEERING, MUMBAI
DEPARTMENT OF MECHANICAL ENGINEERING
END SEMESTER EXAMINATION, JUNE 2023
PROGRAM: Final B.Tech. (Mechanical), Semester-VI
COURSE: OE-BTM611- Computational Methods
TotalPoints: 100
Duratíon: 3 HOURS
Note:
" Answer any 5questions out of 7questions. Each question carries 20 points,
" Answer should be very specific and to the point,
" Make suitable assumptions if needed,
" Answer of all sub-questions must be grouped together in answer book.
" Data in the last column represents course outcome and Blooms Taxonomy of respective question.
CO/BL
Q1. What is the need of numerical integration in the engineering applications? What do 20 2/34
you understand by Newton Cotes Quadrature formula? Suggest any three popular
methods under this class. Which method can give most accurate approximation.
Evaluate the integral (V1+ cos²xdx with help of Trapezoidal and Simpson 1/3
rule with spacing h=0.1
Q2. Differentiate between Interpolation and Regression. 20 1,2/1,3
Following are the census details of the population of India from the year 1961 to
2011, Fit an exponential curve, y=aebk to these data, and hence find the approximate
population in the year 1966, 1985, 1996 and 2009.
Year () 1961 1971 1981 1991 2001 2011
a(mm)/°C 43.9235 54.8160 68.332984.6421 102.8737 121.0193
Is the current regression model for the given data is appropriate? Suggest an
alternative regression model.
20 2,3/1,4
Q3. Consider following partial difference equation 2 =0. Use second order finite
difference equation to find the unknown values uy,uy 13,and us, Use Gauss Seidel
method for the solution.
10
5 10
10 15
10 15
Q4. Differentiate between IVP and BVP with real life example. Name single step and multi- 20 1,2,3
step method (2 methods for each). /1,2,3
Solve the first order ordinary differential equation =y-3t subject to initial
dt
condition y0)= 1, Use RK4 with a step size of h= 0.1 and obtain the solution till t=
0.5 in tabular for with details of steps of calculation.
Discuss the error by comparing the numerical solution with the exact solution given
by yexact =3t' +6t +6-5e.
20 1,3
modelling?
Q5. What do you understand by mathematical modelling and numerical /1,3,4
Explain your understanding with appropriate and sufficient examples.
laboratory and obtained following data
A researcher performed an experiment in his data, construct a
represented in the able where he changed the input (x). Using
polynomial of second order.
Lagrange polynomial and a Newton's divided difference
Calculate f(3) under both methods.
Comment on the order of polynomial possible with the available data.
1 2 4 5 6
X
14 15 5 6 19
f(x) 1
Suggest a technique to ill 20 1,2,3
Q6. What do understand by a system of ill-conditioned system?
3,4
condition problem.
Solve the following system of equations correct to two decimal places.
3.1X+9.4x,-1.5X, = 22.9
2.1x-1.5x, +8,4X, =28.8
6.7x, +1.1x, +2.2x, =20.5
Use following methods to formulate and compare the result,
a. Gauss-Seidel method
b.SUR with relaxation factor = 0.7
Show result in tabular form for minimum six iterations.
Q7. During modelling an engineering system, following transcendental equation emerges 20 1,2/3,4
xe -2=0
Solve for one of the roots of the equation by the secant method and compare the
result with Newton Raphson method.
Tabulate the result, observe it and analyse. Which method gives faster convergence?
