GATE CE topic:partial-differential-equations PYQs & Answers — Page 2

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topic:partial-differential-equations

Questions 11–19 of 19. Imported answers require independent review unless marked reviewed.

Topic practice 19 questionsPage 2 of 2

The function

satisfies the Laplace equation

on a circular domain of radius

with its center at point

with coordinates

. The value of this function on the circular boundary of this domain is equal to 3.

The numerical value of

is:

Your answerChoose one option.

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The Fourier cosine series of a function is given by:

For

, the numerical value of

is ______. (round off to three decimal places)

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The concentration

of pollutants in a one-dimensional reservoir at position

and time

satisfies the diffusion equation

on the domain

, where

is the diffusion coefficient of the pollutants. The initial condition

is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by

at the boundary points

and

at all times. Consider

, and

. The steady-state concentration

at the center

of the reservoir (in

) is ________. (in integer)

Diagram for Civil Engineering question 48

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In the following partial differential equation,

is a function of

and

, and

and

are functions of

The above equation is

Your answerChoose one option.

a second order linear equation

a second degree linear equation

a second order non-linear equation

a second degree non-linear equation

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The following partial differential equation is defined for

The set of auxiliary conditions necessary to solve the equation uniquely, is

Your answerChoose one option.

three initial conditions

three boundary conditions

two initial conditions and one boundary condition

one initial condition and two boundary conditions

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The Fourier series to represent

for

is given by

The value of

(round off to two decimal places), is

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A one-dimensional domain is discretised into

sub-domains of width

with node numbers

. If the time scale is discretised in steps of

, the forward-time and centered-space finite difference approximation at

node and

time step, for the partial differential equation

Your answerChoose one option.

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The solution at

of the partial differential equation

subject to initial conditions of

and

Your answerChoose one option.

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Consider the following partial differential equation:

For this equation to be classified as parabolic, the value of

must be ____________

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GATE CE topic:partial-differential-equations PYQs

Question 11

Question 30

Question 48

Question 1

Question 4

Question 39

Question 27

Question 37

Question 20