Numerical Analysis and Computer Programming-Numerical Integration [IAS (Admin.) Mains Mathematics]: Questions 1 - 6 of 8
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Question 1
Appeared in Year: 2016
Describe in Detail Subjective▾
For an integral , show that the two – point Gauss Quadrature rule is given by using this rule, estimate (CS Paper 2)
EditExplanation
every Finite interval [a, b] can always be transformed to [-1,1] using the transformation
We consider the integral in the form
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Question 2
Appeared in Year: 2013
Describe in Detail Subjective▾
The velocity of a train which starts from rest is given in the following table. The time is in minutes and velocity is in km/hour.
Estimate approximately the total distance run in 20 minutes by using composite Simpson՚s rule. (CS Paper 2)
EditExplanation
If is the distance covered in t (min) , then
At, the velocity of train
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Question 3
Appeared in Year: 2012
Describe in Detail Subjective▾
Solve the following system of simultaneous equations, using Gauss- Seidel Iterative method: (CS Paper 2)
EditExplanation
…
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Question 4
Appeared in Year: 2013
Describe in Detail Subjective▾
Use Euler՚s method with step size to compute the approximate value of Correct up to five decimal place from the initial value Problem.
(CS Paper 2)
EditExplanation
Here,
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Question 5
Appeared in Year: 2011
Describe in Detail Subjective▾
Calculate (upto 3 places of decimal) by dividing the range into 8 equal parts by Simpson՚s rule. (CS Paper 2)
EditExplanation
We have,
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Question 6
Appeared in Year: 2020
Describe in Detail Subjective▾
Find a quadrature formula
Which is exact for polynomials of highest possible degree. Then use the formula to evaluate
(Paper 2)
EditExplanation
Making the method exact for polynomials of degree up to 2, we obtain
For
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