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CSM258:NUMERICAL METHODS AND COMPUTATION:COS:3935

CSM258:NUMERICAL METHODS AND COMPUTATION:COS:3935

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A numerical approximation to a quantity is given as $\tilde {x}=3.1416$ \tilde {x}=3.1416, while the exact value is $x=\pi$ x=\pi . What type of error is obtained from

$|x-\tilde {x}|?$ |x-\tilde {x}|?

Percentage error

Relative error

Absolute error

Truncation order

None

Which value of $\theta$ \theta produces the Backward Euler method in the unified formulation?

$\theta =\dfrac 12$ \theta =\dfrac 12

$\theta =2$ \theta =2

$\theta =0$ \theta =0

❌

$\theta =1$ \theta =1

None

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Consider

$y''+ x y'+ \sin( y )=0$ y''+ x y'+ \sin( y )=0

Which feature prevents this equation from being linear?

The presence of y''

The presence of xy'

The presence of 0

None

The presence of $\sin( y )$ \sin( y )

✅

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In the classical fourth-order Runge-Kutta method, the four slopes are combined using which weighting pattern?

1,2,3,4

1,2,2,1

1,3,3,1

None

1,1,1,1

The Bisection method starts with the interval [1,5]. What is the midpoint used in the first iteration?

2.5

❌

None

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Suppose f(a)f(b) and the interval [a,b] is used in the Bisection method. After one bisection, what is the maximum possible length of the retained interval?