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Indexes:

Compute the integral of f(x) from a to b.

b

/

[

I f(x) dx

]

/

a

f - double precision

function subprogram defining the integrand function

f(x)

a - lower limit of integration

b - upper limit of integration

epsabs - absolute accuracy requested

epsrel - relative accuracy requested

if epsabs.le.0

and epsrel.lt.max(50*rel.mach.acc.,0.5d-28),

the routine will end with ier = 6.

RETURN

result - approximation to the integral i

result is obtained by applying the 21-point

gauss-kronrod rule (res21) obtained by optimal

addition of abscissae to the 10-point gauss rule

(res10), or by applying the 43-point rule (res43)

obtained by optimal addition of abscissae to the

21-point gauss-kronrod rule, or by applying the

87-point rule (res87) obtained by optimal addition

of abscissae to the 43-point rule.

ier - ier = 0 normal and reliable termination of the

routine. it is assumed that the requested

accuracy has been achieved.

ier.gt.0 abnormal termination of the routine. it is

assumed that the requested accuracy has

not been achieved.

abserr - estimate of the modulus of the absolute error,

which should equal or exceed abs(i-result)

neval - number of integrand evaluations

ERROR INDICATIONS

ier = 1 the maximum number of steps has been

executed. the integral is probably too

difficult to be calculated by dqng.

= 6 the input is invalid, because

epsabs.le.0 and

epsrel.lt.max(50*rel.mach.acc.,0.5d-28).

result, abserr and neval are set to zero.

b

/

[

I f(x) dx

]

/

a

f - double precision

function subprogram defining the integrand function

f(x)

a - lower limit of integration

b - upper limit of integration

epsabs - absolute accuracy requested

epsrel - relative accuracy requested

if epsabs.le.0

and epsrel.lt.max(50*rel.mach.acc.,0.5d-28),

the routine will end with ier = 6.

RETURN

result - approximation to the integral i

result is obtained by applying the 21-point

gauss-kronrod rule (res21) obtained by optimal

addition of abscissae to the 10-point gauss rule

(res10), or by applying the 43-point rule (res43)

obtained by optimal addition of abscissae to the

21-point gauss-kronrod rule, or by applying the

87-point rule (res87) obtained by optimal addition

of abscissae to the 43-point rule.

ier - ier = 0 normal and reliable termination of the

routine. it is assumed that the requested

accuracy has been achieved.

ier.gt.0 abnormal termination of the routine. it is

assumed that the requested accuracy has

not been achieved.

abserr - estimate of the modulus of the absolute error,

which should equal or exceed abs(i-result)

neval - number of integrand evaluations

ERROR INDICATIONS

ier = 1 the maximum number of steps has been

executed. the integral is probably too

difficult to be calculated by dqng.

= 6 the input is invalid, because

epsabs.le.0 and

epsrel.lt.max(50*rel.mach.acc.,0.5d-28).

result, abserr and neval are set to zero.