Numerical Method Question Bank

8/8/2019 Numerical Method Question Bank

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JSPM’S

Imperial College of Engineering and Research ,Wagholi,Pune

Department Of Mechanical EngineeringClass!"E#Mechanical$

Su%!&umerical Method and Optimi'ation

(uestion )an*

UNIT 1: Study of root of Equitation

+ -ind the positi.e root of /0!/1+2 %3 &e4ton Raphson correct to three decimal

places

56se Iteration method to o%tain the root of e7uation /5!8/9:12 4ith accurac3 of

22+

; -ind the root of sin/1/!5 near <15= %3 Regular falsi method’s is in radian do

0 iteration>

0 E<plain t3pes of Errors>

= E<plain Con.ergence and di.ergence in Case of &e4ton!raphson method

: Dra4 a -lo4 Chart for Modified &e4ton raphson method to determine the root

of e7uitation correct up to three decimal places

UNIT 2.Study of Simultaneous Equations

+ Dra4 the flo4 chart for gauss Elimination method>

5 Sol.e the follo4ing %3 using ?auss Elimination 4ith Partial pi.oting

/595/;1=

/+95/590/;1++

!;/+9/5!=/;1 !+5



; Sol.e the follo4ing %3 gauss seidal method up to = iteration

5/9;@9+2@15A+

=/9@!B10A

/98@95B1+=A

0 Sol.e the follo4ing %3 using "homas lgorithm

/95@1;

5/9;@9B10

5@!B1+

= Dra4 "he -lo4 Chart for "homas lgorithm

: Dra4 the -lo4 Chart for ?auss Seidal Metho

UNIT 3 – Optimazation

1. Ma<imi'e B 1 ;<+ <5

Su%ected to <+ 5<5 F 5

5<+ <5 F 0

/+ 9 <5 F =

/+, <5 G 2 6sing Simple< method5 E<plain %riefl3 a%out ad.ance optimi'ation techni7ues #a$ ?enetic

algorithm #%$ Simulated annealing algorithm

; HPP is to ma<imi'e profit function

B 1 =2<+ 9 +8<5

Su%ect to the constraints

5<+ 9 <5 F +22

/+ 9 <5 F 82

/+, <5 G 2

0 Minimi'e C 1 5< 9 =3 su%ect to

< 9 53 G0

;< 9 53 G;

< G 2, 3 G 2

= #a$ What are the re7uirement of liner programming pro%lem



#%$ Construct a liner programming model 4ith suita%le e<ample

UNIT 4 –Study of Cure !ittin"

+ #a$Dra4 a flo4chart for logarithmic cur.e fitting

#%$ In some determinations of the .alue . of car%on dio<ide dissol.ed in a

gi.en .olume of 4ater at different temperatures ,the follo4ing pairs of

.alues 4ere o%tained

2 = +2 +=

+82 +0= ++8 +22

O%tain %3 the method of least s7uare, a relation of the form v1a9b 4hich %est fits

to these o%ser.ations

5 "he pressure and .olume of a gas are related %3 the e7uation PV < 1 *,

< and * %eing constants -it this e7uations for the follo4ing set of o%ser.ations

P#KgLcm5$ 2= + += 5 5= ;

#liters$ +:5 + 2A= 2:5 2=5 20:

#%$Wh3 least s7uare error regression method is preferred o.er other methods of

linear regression >lso e<plain 4h3 s7uaring of error is carried out, if s7uaring of

error is not done 4hat 4ill %e effect on cur.e fitting e7uation

; #a$ Dra4 flo4chart for Hagrange Interpolation method

#%$-ind pol3nomial passing through points #2,+$#+,+$#5,A$#;,5=$#0,:+$#=,+5+$

using &e4tons Interpolation formula and hence find 3 and d3Ld< at <12=

0 "he .alues of <,3 N 3 are gi.en %elo4 6se ermit Interpolation to find .alues

of 3 at <125=

/ @ 3i

2 2 2+ + +

= #a$ -rom the ta%le %elo4 for 4hat .alue of <,3 is minimum>lso find the .alue

of 3



/ ; 0 = : A 8

@ 252= 25022 25=2 25:52 25=22 25502

#%$Dra4 -lo4chart for Hagranges Interpolation

UNIT#$ Numrri%al Inter"ration

+-ind a real root of 5<Qlog+2<1Acorrect to four decimal places using iteration

method

5Dra4 a flo4chart for Simpsons ;L8 rule of integration

; Dra4 flo4chart for gauss!legendre 5!point formula and ;! point formula

0-ind pol3nomial passing through points #2,+$#+,+$#5,A$#;,5=$#0,:+$#=,+5+$ using

&e4tons Interpolation formula and hence find 3 and d3Ld< at <12=

=find the integral of d< %3 trape'oidal rule

UNIT#& Numeri%al Solution Of 'ifferential Equitation

+ "he second order ODE is transformed into pair of first!order ODEs as in d3Ldt1'3#2$15 d'Ldt12=<Q3 '#2$12 Estimate the .alue of ' and 3 at <125 4ith step

si'e of 2+

5 6sing Runge ! Kutta method of fourth order, sol.e d3Ld<135Q<5L35 9 <5 4ith 3#2$

1 +

at < 1 25, 20

; E<plain predictor and corrector method to sol.e ordinar3 differential e7uation

and also dra4 corresponding flo4 chart

0 What is meant %3 order of Runge!Kutta method> nd compare RK methods 5nd

order ,;rd

order and 0th order graphicall3

=Dra4 a flo4chart for RK Second order method

Numerical Method Question Bank

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