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

University of Delhi Mathematical Methods for Numerical Analysis and Optimization

Previous Year QP for Numerical Analysis

Typology: Exams

2024/2025

Uploaded on 06/05/2025

zenith-lal 🇮🇳

1 document

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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

(1000) P.T.O.

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.

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

Use of non-programmable scientific calculator is allowed.

Write your^ Roll No. on the top i t

(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)

(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

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)

polynomials for the function f(x) defined by the

data :

P. T. O.

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

Related documents

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

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

G

u\a^ ir^ Coile

Duration : 3 Hours

of this question paper.

Write your^ Roll No. on the top i t

(1000) P.T.O.

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

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

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

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

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

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

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

extrapolate from^ these values^ using^ Richardson

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

P,T.O.

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

the system of equations :

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

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

the system of equations :

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

(a) Construct the Lagrange form of the interpolating

polynomial from the following data :

(b) Construct the divided difference table for the

following data set and then write out the Newton

form of the interpolating polynomial.

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

polynomials for the function f(x) defined by the