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Quad_qawc Calculator

Quad_qawc

Function: quad_qawc (<f(x)>, <x>, <c>, <a>, <b>, [<epsrel>, <epsabs>, <limit>])

Function: quad_qawc (<f>, <x>, <c>, <a>, <b>, [<epsrel>, <epsabs>, <limit>]) Computes the Cauchy principal value of f(x)/(x - c) over a finite interval. The strategy is globally adaptive, and modified Clenshaw-Curtis integration is used on the subranges which contain the point x = c.

quad_qawc computes the Cauchy principal value of

integrate (f(x)/(x - c), x, a, b)

using the Quadpack QAWC routine. The function to be integrated is <f(x)>/(<x> - <c>), with dependent variable <x>, and the function is to be integrated over the interval <a> to <b>.

The integrand may be specified as the name of a Maxima or Lisp function or operator, a Maxima lambda expression, or a general Maxima expression.

The keyword arguments are optional and may be specified in any order. They all take the form key=val. The keyword arguments are:

<epsrel> Desired relative error of approximation. Default is 1d-8.

<epsabs> Desired absolute error of approximation. Default is 0.

<limit> Size of internal work array. <limit> is the maximum number of subintervals to use. Default is 200.

quad_qawc returns a list of four elements:

* an approximation to the integral,

* the estimated absolute error of the approximation,

* the number integrand evaluations,

* an error code.

The error code (fourth element of the return value) can have the values:

0 no problems were encountered;

1 too many sub-intervals were done;

2 excessive roundoff error is detected;

3 extremely bad integrand behavior occurs;

6 if the input is invalid.

Examples:

          (%i1) quad_qawc (2^(-5)*((x-1)^2+4^(-5))^(-1), x, 2, 0, 5,
                           epsrel=1d-7);
          (%o1)    [- 3.130120337415925, 1.306830140249558E-8, 495, 0]
          (%i2) integrate (2^(-alpha)*(((x-1)^2 + 4^(-alpha))*(x-2))^(-1),
                x, 0, 5);
          Principal Value
                                 alpha
                  alpha       9 4                 9
                 4      log(------------- + -------------)
                                alpha           alpha
                            64 4      + 4   64 4      + 4
          (%o2) (-----------------------------------------
                                  alpha
                               2 4      + 2

3 alpha 3 alpha ------- ------- 2 alpha/2 2 alpha/2 2 4 atan(4 4 ) 2 4 atan(4 ) alpha - --------------------------- - -------------------------)/2 alpha alpha 2 4 + 2 2 4 + 2

          (%i3) ev (%, alpha=5, numer);
          (%o3)                    - 3.130120337415917

(%o1)                                true
(%i2) 

Quad_qawc Example

Related Examples

quad_qawc

? quad_qawc;

Calculate

quad_qawc

? quad_qawc;

Calculate