STM Article Repository

In this paper, we present two methods: Modified Clenshaw-Curtis and the Gauss-Jacobi methods. These methods are commonly used in the evaluation of the finite Fourier transforms of integrands with endpoint singularities. In the first method, the integrand is truncated by the Chebyshev series, term by term, and then its singularity types are evaluated using recurrence relations. This method is more efficient for low-frequency values. On the other hand, the Gauss Jacobi method is found to be accurate in the evaluation of integrals with fairly high-frequency values; such as 1000. MATHEMATICA codes, for both methods, are provided for the purpose of testing the efficiency of automatic computation. Lastly, the illustrative examples are considered with regards to reliability, accuracy, and comparison of the methods outlined.