Page 228 - Engineering Mathematics Workbook_Final

Numerical Methods

decimal places) of flow of 2 exact solution and the solution
downstream section at x = 1m from obtained using a single iteration of
one calculation step of Single Step the second-order Runge-Kutta
Euler Method is _________. method with step-size h = 0.1 is.

[GATE-2018 (CE-MORNING SESSION)] [GATE-2016-EC-SET 3]

BACKWARD EULER METHOD RUNGE-KUTTA METHOD OF

TH
108. The differential equation 4 ORDER
dy = 0.25y is to be solved using 111. Consider an ordinary differential
2
dx dx
the backward (implicit) Euler’s equation = 4t + 4 . If x = x at t =
0
method with the boundary condition dt

y = 1 at x = 0 and with a step size of 0, the increment in x calculated using
1. What would be the value of y at x Runge-Kutta fourth order multistep
method with a step size of t 
= 1? = 0.2
is
(a) 1.33 (b) 1.67
(a) 0.22 (b) 0.44
(c) 2.00 (d) 2.33
(c) 0.66 (d) 0.88
[GATE-2006]
[GATE-2014-ME-SET 4]

MODIFIED EULER METHOD
GAUSS SEIDAL AND
109. Given the differential equation
y = 1 x − y with initial condition y(0) GAUSS JACOBI METHOD

= 0. The value of 112. Gauss-Seidel method is used to solve
the following equations (as per the
y(0, 1) calculated numerically upto given order):
nd
the third place of decimal by the 2
5
order Runge Kutta method with step x + 2x + 3x = ,
3
2
1
size h = 0.1 is 2x + 3x + x = 1,
1
3
2
[GATE-1993 (ME)] 3x + 2x + x = 3
1
3
2
110. Consider the first order initial value Assuming initial guess as
−
problem y = + 2x x , y(0) = 1, x = x = x = 0 , the value of x after
2
1
y
3
1
2
3
)
x
(0    with exact solutions the first iteration is _____
x
y ( ) x = x + 2 e . For x = 0.1, the [GATE-2016]
percentage difference between the

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