Comparison of Romberg and Gauss methods for numerical evaluation of twodimensional phase integrals
Abstract
The double integral used in the investigation forms a part of most scattered field integrals. An evaluation of the accuracy of a numerical integration can be based on a closedform solution of the integral. The integral was numerically evaluated by two principal algorithms. The first was Romberg integration applied consecutively on inner and outer integrals. This involves the application of the trapezoidal rule. The second algorithm was Gauss quadrature, which was also consecutively applied on inner and outer integrals, taking into account GaussLegendre formulas. It was found that for the same number of integration points the Gauss quadrature method is much more accurate than the Romberg method. Also, for the corresponding error limits the Gauss quadrature method needs fewer integration points and, therefore, requires much less computer time.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 July 1977
 DOI:
 10.1109/TAP.1977.1141637
 Bibcode:
 1977ITAP...25..581C
 Keywords:

 Algorithms;
 Electromagnetic Scattering;
 Entire Functions;
 Error Analysis;
 Numerical Integration;
 Run Time (Computers);
 Antenna Radiation Patterns;
 Computer Programs;
 Phase Shift;
 Radiation Distribution;
 Reflectors;
 Scattering Functions;
 Communications and Radar