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Dear students, this is to inform that GDB will be started on February 6, 2013 at 00:00 and will be closed on February 7, 2013 at 23:59.
The topic for Graded Moderated Discussion Board is
“Compare the efficiency and characteristics of methods available to you for numerical integration.”
It is necessary for every student to take part in this discussion board. Your comments will be graded, which is worth 5% of your total marks.
You should remember that you have to post your comments about the discussion title with in the time
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NUMERICAL INTEGRATION (“Compare the efficiency and characteristics of methods available to you for numerical integration.”)
In numerical analysis, the Newton–Cotes formulae, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally-spaced points. They are named after Isaac Newton and Roger Cotes.
Newton–Cotes formulae can be useful if the value of the integrand at equally-spaced points is given. If it is possible to change the points at which the integrand is evaluated, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are probably more suitable.
In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. (See numerical integration for more on quadrature rules.) An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the points x_{i} and weights w_{i} for i = 1,...,n. The domain of integration for such a rule is conventionally taken as [−1, 1], so the rule is stated as
In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, andFaulhaber's formula for the sum of powers is an immediate consequence
some imp methods
Forward Euler
Hamming Midpoint
Backward Euler
Trapezoidal
Parabolic
Sirnpson's Rule
Corrected Trapezoidal
Romberg Integration
Gear's Integration Methods
Bode's Integration Methods
Gaussian Quadrature
Milne's PredictorICorrector
Newton-Cotes
runge-KtUta
mth603 gdb# 1
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