ROMBERG
Integral Estimation using Repeated Quadrature and Extrapolation

ROMBERG is a FORTRAN90 library which estimates the integral of a function f(x) over an interval [a,b] using one of:

• the trapezoidal rule;
• the composite trapezoidal rule;
• a sequence of composite trapezoidal rules;
• a sequence of composite trapezoidal rules and Romberg extrapolation.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ROMBERG is available in a FORTRAN90 version.

Related Data and Programs:

CLENSHAW_CURTIS_RULE, a FORTRAN90 program which defines a Clenshaw Curtis quadrature rule.

INTLIB, a FORTRAN90 library which contains a variety of routines for numerical estimation of integrals in 1D.

QUADPACK, a FORTRAN90 library which contains a variety of routines for numerical estimation of integrals in 1D.

QUADRULE, a FORTRAN90 library which defines quadrature rules for 1D domains.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.

Source Code:

• romberg.f90, the source code.

Examples and Tests:

• romberg_test.f90, a sample calling program.
• romberg_test.txt, the output file.

List of Routines:

• ROMBERG_TRAP approximates an integral by extrapolating the trapezoidal rule.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRAPEZOID carries out the composite trapezoid rule.
• TRAPEZOID_REFINE carries out a step of trapezoidal refinement.
• TRAPEZOID_TOL repeatedly refines the trapezoid rule til a tolerance is met.

You can go up one level to the FORTRAN90 source codes.