Numerical Analysis-Summation Formula (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 3 of 3

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Question number: 1

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

Essay Question▾

Describe in Detail

By using Euler-Maclaurin formula, find the sum

Equation

Explanation

The Euler-Maclaurin formula is

Equation

where

Equation

Given the equation

Equation

Equation

Equation

Question number: 2

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation Equation with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Explanation

The given differential equation is

Equation

with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Using Euler’s method,

Equation

where

Equation

So, putting the initial condition, when n = 0

Equation

Equation

Equation

and

Equation

Equation

Now first modification of y 1

Equation

Equation

… (25 more words) …

Question number: 3

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Solve the equation:

Equation

Use Euler algorithm and tabulate the solution at x = 0.1, 0.2, 0.3.

Explanation

The given differential equation is

Equation

with initial condition x 0 = 0, y 0 = 0

Using Euler, s method,

Equation

where

Equation

We obtain y at x = 0.1

Equation

Equation

Equation

Again obtain y at x = 0.2

Equation

Equation

Equation

Similarly y at x = 0.3

… (18 more words) …

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