Oscillatory Quadratures Based on the Tau Method

Mohamed K. El Daou


In this paper we discuss the integration of highly oscillatory univariate and multivariate functions. Based on the recursive formulation of the Tau method we develop numerical quadratures that achieve a high degree of accuracy when the frequency in the integrand takes moderate as well as very large values. With our procedures the integral is obtained in terms of the value of the function and its derivatives at the boundary points. The accuracy of our results are confirmed through numerical examples.

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DOI: http://dx.doi.org/10.5539/jmr.v5n3p56

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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