Let \({ X }^{ 2 }-117=0.\) The iterative steps for the solution using Newton-Raphson's method is given by
A\({ X }_{ k+1 }=\frac { 1 }{ 2 } \left( { X }_{ k }+\frac { 117 }{ { X }_{ k } } \right) \)
B\({ X }_{ k+1 }={ X }_{ k }-\frac { 117 }{ { X }_{ k } } \)
C\({ X }_{ k+1 }={ X }_{ k }-\frac { { X }_{ k } }{ 117 } \)
D\({ X }_{ k+1 }={ X }_{ k }-\frac { 1 }{ 2 } ({ X }_{ k }+\frac { 117 }{ { X }_{ k } } )\)
Question - 2
Equation \({ e }^{ x }-1=0\) is required to be solved using Newton's method with an initial guess \({ X }_{ o }=-1\) . Then after one step of Newton;s method, estimate x1 of the solution will be given by
A0.71828
B0.36784
C0.2.587
D0.000
Question - 3
The square root of a number N is to be obtained by applying the Newton-Raphson iteration to the equation \({ X }^{ 2 }-N=0\) . If I denotes the iteration index the correct iterative scheme will be
A\({ X }_{ i+1 }=\frac { 1 }{ 2 } \left( { X }_{ i }+\frac { N }{ { X }_{ i } } \right) \)
B\({ X }_{ i+1 }=\frac { 1 }{ 2 } \left( { X }^{ 2 }_{ i }+\frac { N }{ { X }^{ 2 }_{ i } } \right) \)
C\({ X }_{ i+1 }=\frac { 1 }{ 2 } \left( { X }_{ i }+\frac { N^{ 2 } }{ { X }_{ i } } \right) \)
D\({ X }_{ i+1 }=\frac { 1 }{ 2 } \left( { X }_{ i }+\frac { N }{ { X }_{ i } } \right) \)
Question - 4
Gauss-Seidel iterative method can be used for solving a set of
Alinear differential equation only
Blinear algebraic equations only
CBoth linear and non-linear algebraic equations
DBoth linear and non-linear differential equations
Question - 5
The convergence of the bisection method is
Acubic
Bquadratic
Clinear
DNone of these
Question - 6
For the differential equation \(\frac { dy }{ dx } =x-{ y }^{ 2 }\) is given that
X
0
0.2
0.4
0.6
Y
0
0.02
0.0795
0.1762
Using predictor-correction method, the y at next value of x is
A0.5114
B0.4648
C0.3046
D0.2498
Question - 7
Which one of the following is correct?
ABisection method is used for iteration
BRegula-falsi method is direct method
CSecant method is direct method
DNewton-Raphson method is not iterative method
Question - 8
if n=3, ao=1, a1=0, a2 = -1, a3 = -11, then the root of the equation between 2 and 3 by regular-falsi method is
A2.0
B2.09
C2.9
D2.2
Question - 9
If \({ e }^{ o }=1,{ e }^{ 1 }=2.72,{ e }^{ 2 }=7.39,{ e }^{ 3 }=20.09\) and \({ e }^{ 4 }=54.60\) , then by Simpson's \(\frac { 1 }{ 3 } rd\) rule value of \(\int _{ 0 }^{ 4 }{ { e }^{ x } } dx\) is
A52.78
B53.87
C5.278
D5.387
Question - 10
Match the items in Columns I and II using the codes given below the columns.
