double TrapezoidQuadrature	(	double(*)(double)	f,
		double	x0,
		double	xn,
		int	n
	)

Integrates f with composite trapezoid rule.

Parameters

f	Function to integrate takes a double argument, x, and returns a double value
x0	The lower integration domain limit.
xn	The upper integration domain limit.
n	The number of intervals into which to break the domain.

Returns: The numerical approximation for $\int_{x_0}^{x_n}{f(x)}{dx}$ .

With $h = \frac{(x_n - x_0)}{n}$ , and $x_i = x_0 + {i}{h}$ , the integral is calculated as:

$\int_{x_0}^{x_n}{f(x)}{dx} \approx \frac{h}{2}\sum_{i=1}^{n}(f(x_{i-1}) + f(x_i))$

The error of this method is $O(h^2)$ .

Test:: ElmerFoamFSI::TestingObject::Test__TrapezoidQuadrature tests this function by sending linear and quadratic test functions.

Definition at line 39 of file src/ExampleSourceFile.C.

Referenced by TestingObject< ResultsType >::Test__TrapezoidQuadrature().

   {
     double h = (xn - x0)/(static_cast<double>(n));
     if(std::fabs(h) < 1e-12) throw 1;
     double sum = .5*(f(x0)+f(xn));
     for(int i = 1; i < n;i++)
       sum += f(x0 + i*h);
     return(h*sum);
   };

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