MTH603 Quiz 1 Solution and Discussion

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To improve the accuracy of the derivative of the function, which of the following method is more helpful? MTH603

Extrapolation
Interpolation
Divided difference
Central difference

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For a function ‘f(x) = x’, with a step size of ‘h=0.01’, which of the following gives the 1st derivative at x =1 by using two point formula? MTH603

Y’=(x)=1+Some truncation Error

Y’=(x)=1.01+Some truncation Error

Y’=(x)=.0.1+Some truncation Error

Y’=(x)=0.1+Some truncation Error

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While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ? MTH603
(y2 + y4)/2
(y2 + y4)
(y2 - y4)/2
(y2 - y4)

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In Newton-Cotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral? MTH603

Trigonometric Function

Exponential Function

Logarithmic Function

Polynomial Function Page=166

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3rd

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Richardson extrapolation is method also known as ………… MTH603
Sequence acceleration method
Series acceleration method

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In Simpson’s 1/3 rule, the global error is of ……………… MTH603

O(h2)

O(h3)

O(h4) Page=171

Non of the given choices

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δ = E 1/2 - E 1/2

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Sequence acceleration method

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.

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zaasmi

@zareen said in MTH603 Quiz 1 Solution and Discussion:

Series acceleration method

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.
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zaasmi

@zareen said in MTH603 Quiz 1 Solution and Discussion:

In Newton-Cotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral? MTH603

In numerical analysis, Simpson’s method is a method for numerical integration, the numerical approximation of definite integrals. … Simpson’s rule also corresponds to the three-point Newton-Cotes quadrature rule

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zaasmi

@zareen said in MTH603 Quiz 1 Solution and Discussion:

Trigonometric Function

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

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dy/dx - = 1 - y,y(0) = 0 is an example of

In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval

The (n + 1) th difference of a polynomial of degree n is...

Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by

In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be

In fourth order Runge-Kutta method K 4

In fourth order Runge-Kutta method k2

What is the Process of finding the values outside the interval (Xo,x,) called?

When we apply Simpson's 3/8 rule, the number of intervals n must be

Milne's P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past --equally spaced points.

The truncation error in Adam's predictor formula is ....-times more than that in corrector formula

To apply Simpson's 3/8 rule, the number of intervals be

Which formula is useful in finding the interpolating polynomial?

Rate of change of any quantity with respect to another can be modeled by

Romberg's integration method is ------ than Trapezoidal and Simpson's rule.

In integrating f, e2* dx by dividing into eight equal parts, width of the interval should be......

To apply Simpson's 1/3 rule, valid number of intervals are?

Newton's divided difference interpolation formula is used when the values of the independent variable are

If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree

MTH603 Assignment 1 Solution and Discussion

MTH603 Quiz 1 Solution and Discussion

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