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Numerical Analysis PYQ, Exams of Mathematical Methods for Numerical Analysis and Optimization

University of DelhiMathematical Methods for Numerical Analysis and Optimization

Previous Year QP for Numerical Analysis

Typology: Exams

2024/2025

Uploaded on 06/05/2025

zenith-lal
zenith-lal 🇮🇳

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4469 8[This question paper contains 8 printed pages.]
Your Roll No.....,..,...,..
Sr, No. of Question Paper: 4469
Unique Paper Code 32357501
Name of the Paper DSE-I Numerical Analysis
(LOCF)
Namc of the Course B.Sc. (Hons.) Mathematics
S em e ster
*=r.i, 1<t<2,x(1)=1 taking the step size as G
h : 0.5. (6 s)
ir Coile
\au
Duration : 3 Hours
Instructions for Candidates
mum Mar S.L
I(*
elp
of this question paper.
2. All six questions are compulsory.
3. Attempt any two parts from each question.
Use of non-programmable scientific calculator is
allowed.
Write your Roll No. on the top it
4
(1000) P.T.O.
pf3
pf4

Partial preview of the text

Download Numerical Analysis PYQ and more Exams Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity!

4469 8 [This question paper contains 8 printed pages.]

Your Roll No.....,..,...,..

Sr, No. of Question Paper: 4469

Unique Paper Code 32357501

Name of the Paper DSE-I Numerical Analysis

(LOCF)

Namc of the Course B.Sc. (Hons.) Mathematics

S em e ster

*=r.i,

1<t<2,x(1)=1 taking the step size as

G

h :^ 0.5. (^) (6 s)

u\a^ ir^ Coile

Duration : 3 Hours

Instructions (^) for Candidates

mum Mar S .L I (^) (*

elp

of this question paper.

  1. All six questions are compulsory.
  2. Attempt any two parts (^) from each question.

Use of non-programmable scientific calculator is allowed.

Write your^ Roll No. on the top i t

4

(1000) P.T.O.

(a) Discuss the order of convergence of^ the^ Newton

Raphson method. (6)

(b) Perform three iterations of^ the Bisection^ method

in the interval (1,2)^ to obtain^ root of^ the^ equation

x3-x-l:0. (6)

(c) Perform three iterations of^ the^ Secant^ method to

obtain a root of the equation x2^ - 7 :^ O^ with initial

approximations xo: 2,^ x,^ : 3.^ (6)

(a) Perform three iterations of False^ Position^ method

to find the root of the equation x3^ - 2 :^0 in^ the

interval (1,^ 2). (6.5)

(b) (^) Find a root of the equation x3 5x +^1 :^0 correct

up to three places^ of decimal by^ the^ Newton's

(c) Approximate the derivative of f(x) = 1 +^ x^ +^ x3^ at

xo:0 using the first order forward^ difference

formula taking h^ :^ V., %^ and 1/8^ and^ then

extrapolate from^ these values^ using^ Richardson

extrapolation. (6)

  1. (a) Using the trapezoidal^ rule,^ approximate the^ value

of the integral J'm* a*^.^ Verify^ that^ the^ theoretical

(b) Derive the Simpson's l/3'd rule^ to^ approximate

the integral^ of^ a^ function.^ (6.s)

(c) Apply the modified Euler method^ to^ approximate

the solution of the initial value problem

) 7

2

P,T.O.

error bound holds.

(

(b) Set up the Gauss-Jacobi iteration scheme to solve

the system of equations :

5x,+xr+2xr=

-3x, f^ 9x,^ +^ 4xr:^ -

xr t^ 2xz (^) - 7xt: (^) -

Take the initial approximation as X(0) = (0,0,0)^ and

do three iterations. (6.5 )

(c) Set up the Gauss-Seidel iteration scheme to solve

the system of equations :

6xr-2xr+x,=

-2x, *^ 7x.,^ +^ 2x3:^5

xr*2xr-5xr:-

Take the initial approximation as^ 1{0)^ = (1,0,0)

and do three iterations. (6.5)

(a) Construct the Lagrange form of the interpolating

polynomial from the following data :

x 0 I^ J r(*) I 3 55

(6)

(b) Construct the divided difference table for the

following data set and then write out the Newton

form of the interpolating polynomial.

x 0 I 2 v -1 0 l5^80

Hence, estimate the value of f(1.5) (6)

(c) (^) Obtain the piecewise linear interpolating

polynomials for the function f(x) defined by the

data :

4

P. T. O.