COMPUTATIONAL EFFICIENCY OF SINGULAR AND OSCILLATORY INTEGRALS WITH ALGEBRAIC SINGULARITIES | Asian

We describe two approaches in this paper: modified Clenshaw-Curtis and Gauss-Jacobi. These methods are often utilised in the evaluation of integrands with endpoint singularities' finite Fourier transformations. The integrand is truncated by the Chebyshev series term by term in the first technique, and then its singularity types are determined using recurrence relations. For low-frequency data, this technique is more efficient. The Gauss Jacobi approach, on the other hand, is proven to be correct in the evaluation of integrals with relatively high-frequency values, such as 1000. Both systems have MATHEMATICA codes that can be used to verify the efficiency of automatic computing. Finally, the illustrative instances are evaluated in terms of the methodologies' reliability, correctness, and comparability.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/4194