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A variable interval width quadrature technique based on Romberg's method

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
5
Issue
2
Identifiers
DOI: 10.1016/0021-9991(70)90063-x
Disciplines
  • Computer Science

Abstract

Abstract A numerical integration or quadrature technique (based on Richardson extrapolation to the trapezoidal rule as formulated by Romberg) was developed and applied to evaluate some Fourier integrals which occur in the theory of an infinite cylindrical antenna. The computational method is based on an abscissa spacing which varies as powers of two and which is determined by the relative convergence of two successive approximations to the integral over a given interval. This results in a minimum-to-maximum abscissa spacing ratio as small as 10 −6. Numerical examples are given for integration contours following the real axis and deforming into the complex plane.

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