Page 220 - Engineering Mathematics Workbook_Final

Numerical Methods

59. Consider the first order initial value (III) Simphson’s Rule
−
problem y = + 2x x , ( ) 0 = , (IV) Runge-Kutta
2
1
y
1
y
)
x
(0    with exact solutions
Choose the correct set of
x
y ( ) x = x + 2 e . For x = 0.1, the combinations.
percentage difference between the
exact solution and the solution (a) P – II, Q – I, R – III, S - IV
obtained using a single iteration of (b) P – I, Q – II, R – IV, S – III
the second-order Runge-Kutta
method with step-size h = 0.1 is. (c) P – IV, Q – III, R – II, S – I

[GATE 2016 – EC – SET-3] (d) P – II, Q – I, R – IV, S – III

du [GATE 2017 (CH)]
60. Consider the equation = 3t + 2 1
dt 63. Variation of water depth (y) in a
with u = 0.1 at t = 0. This is gradually varied open channel flow is
numerically solved by using the given by the first order differential
forward Euler method with a step equation
size. t  = 2. The absolute error in
10
the solution at the end of the first dy 1 e 3 ln y
−
time step is __________. = −
−
dx 250 45e 3ln y
[GATE 2017 – CE – SESSION-1]
Given initial combination y (x = 0) =

61. Match the problem type in Group – 1 0.8 m. The depth (in m, up to three
with the numerical method in Group decimal places) of flow at a
– 2 downstream section at x = 1m from
one calculation step of Single Step
Group – 1 Euler Method is _______

(P) System of linear algebraic [GATE 2018 ( ME – Morning Session)]
equations
64. An explicit forward Euler method is
(Q) Non-linear algebraic equations
used to numerically integrate the

(R) Ordinary differential equations differential equation dy = y using a
dt
(S) Numerical integrations
time step of 0.1. With the initial

Group – 2 condition y(0) = 1, the value of y(1)
computed by this method is
(I) Newton-Raphson __________ (correct to two decimal

(II) Gauss-seidel places).

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