Numerical analysis of a fast integration method for highly oscillatory functions
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The integration of systems containing Bessel functions is a central point in many practical problems in physics, chemistry and engineering. This paper presents a new numerical analysis for the collocation method presented by Levin for \(\int_a^b f(x)S(rx)dx\) and gives more accurate error analysis about the integration of systems containing Bessel functions. The effectiveness and accuracy of the quadrature is tested for Bessel functions with large arguments.
Key wordsoscillatory integrals Bessel function error bounds collocation method
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- 1.M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York, 1965.Google Scholar
- 2.P. I. Davis and P. Rabinowitz, Methods of Numerical Integral Integration, 2nd edn., Academic Press, 1984.Google Scholar
- 3.L. N. G. Filon, On a quadrature formula for trigonometric integrals, Proc. R. Soc. Edinb., 49 (1928), pp. 38–47.Google Scholar
- 9.D. Levin, Analysis of a collocation method for integrating rapidly oscillatory functions, J. Comput. Appl. Math., 78 (1997), pp. 131-138.Google Scholar