Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space
نویسندگان
چکیده
Computation of integrals of strongly oscillating functions is one of the more important problems of numerical analysis, because such integrals are encountered in applications in many branches of mathematics as well as in other science such as quantum physics, flow mechanics and electromagnetism. Main examples of strongly oscillating integrands are encountered in different transformation, for example, the Fourier transformation and Fourier-Bessel transformation. Standard methods of numerical integration frequently require more computational works and they cannot be successfully applied. The earliest formulas for numerical integration of rapidly oscillatory functions were given by Filon [3] in 1928. The Filon’s approach for Fourier integrals
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