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

Integrates f with composite midpoint 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 $x_i = x_0 + h(i-\frac{1}{2})$ , the integral is calculated as:

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

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

Test:: ElmerModuleDriver::TestingObject::Test__MidPointQuadrature tests this function by sending linear and quadratic test functions.

Definition at line 51 of file Third_Party_Modules/ElmerFSI/trunk/src/ExampleSourceFile.C.

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

   {
     double h = (xn - x0)/(static_cast<double>(n));
     if(std::fabs(h) < 1e-12) throw 1;
     double sum = 0.0;
     for(int i = 1;i <= n;i++)
       sum += f(x0+((static_cast<double>(i)-.5)*h));
     return(h*sum);
   }

Here is the caller graph for this function: