a = quad('function',a,b)
a = quad('function',a,b,tol)
a = quad('function',a,b,tol,trace)
a = quad8('function',a,b)
a = quad8('function',a,b,tol)
a = quad8('function',a,b,tol,trace)
quad
and quad8
implement two different quadrature algorithms. quad
implements a low order method using an adaptive recursive Simpson's rule. quad8
implements a higher order method using an adaptive recursive Newton-Cotes 8 panel rule.
q = quad('function',a,b)
returns the result of numerically integrating the function fun(x)
between the limits a
and b
. The function function
must return a vector of output values when given a vector of input values.
q = quad('function',a,b,tol)
iterates until the relative error is less than tol
. The default value for tol
is 1e-3.
If the final argument trace
is nonzero, quad
plots a graph showing the progress of the integration.
quad8
has the same calling sequence as quad
.
a = quad('sin',0,pi)
a =
2.0000
quad
uses an adaptive recursive Simpson's rule. quad8
uses an adaptive recursive Newton-Cotes 8 panel rule. quad8
is better than quad
at handling functions with soft singularities:
quad
and quad8
have recursion level limits of 10 to prevent infinite recursion for a singular integral. Reaching this limit in one of the integration intervals produces the warning message:
The computation continues using the best value available in that interval.Recursion level limit reached in quad.
Singularity likely.
quad
nor quad8
is set up to handle integrable singularities:
If you need to evaluate an integral with such a singularity, recast the problem by transforming the problem into one in which you can explicitly evaluate the integrable singularities and let quad
or quad8
take care of the remainder.
quaddemo
demonstration program
(c) Copyright 1994 by The MathWorks, Inc.