GATE CE topic:numerical-methods PYQs & Answers — Page 2

Questions 11–20 of 21. Imported answers require independent review unless marked reviewed.

Consider the differential equation

For the initial condition

, the value of

obtained using Euler’s method with a step-size of 0.2 is ________. (round off to one decimal place)

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The value of

using the trapezoidal rule with four equal subintervals is

Your answerChoose one option.

1.718

1.727

2.192

2.718

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The values of abscissa (

) and ordinate (

) of a curve are as follows:


2.0	5.00
2.5	7.25
3.0	10.00
3.5	13.25
4.0	17.00

By Simpson’s 1/3rd rule, the area under the curve (round off to two decimal places) is ________

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Numerically integrate,

from lower limit

to upper limit

. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is

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The true value of

is 0.69. If the value of

is obtained by linear interpolation between

and

, the percentage of absolute error (round off to the nearest integer), is

Your answerChoose one option.

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The integral

is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson’s rules with a common step size. In this context, which one of the following statements is TRUE?

Your answerChoose one option.

Simpson’s rule as well as rectangular rule of estimation will give NON-zero error.

Simpson’s rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.

Only the rectangular rule of estimation will give zero error.

Only Simpson’s rule of estimation will give zero error.

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A continuous function

is defined. If the third derivative at

is to be computed by using the fourth order central finite-difference scheme (with step length = h), the correct formula is

Your answerChoose one option.

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The value of the function

is given at

distinct values of

and its value is to be interpolated at the point

, using all the

points. The estimate is obtained first by the Lagrange polynomial, denoted by

, and then by the Newton polynomial, denoted by

. Which one of the following statements is correct?

Your answerChoose one option.

is always greater than

and

are always equal

is always less than

No definite relation exists between

and

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The quadratic equation

is to be solved numerically starting with an initial guess as

. The new estimate of x after the first iteration using Newton-Raphson method is _____

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Variation of water depth (

) in a gradually varied open channel flow is given by the first order differential equation

Given initial condition:

m. The depth (in m, up to three decimal places) of flow at a downstream section at

m from one calculation step of Single Step Euler Method is _____

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GATE CE topic:numerical-methods PYQs

Question 48

Question 27

Question 36

Question 46

Question 3

Question 3

Question 27

Question 18

Question 20

Question 39