Numerical Approximation of Highly Oscillatory Integrals with Weak Singularity

Year 2019, Volume: 2 Issue: 2, 61 - 71, 30.12.2019

İrfan Ullah Muhammad Munib Khan

Abstract

In this paper, we design an accurate scheme for the approximation of highly oscillatory integrals having singularity . The interval of integration [a,b] is divided into two subintervals and then approximate the integral over first interval by hybrid function quadrature (Q_hf [g]), while for the approximation of integrals over the second interval we use Levin meshless method (Q_L^m [g]). For a result, we find the sum of both the integrals. To check the effectiveness of method results of some test problems are calculated by hybrid function quadrature and compared with the results produces by the proposed method.

Keywords

oscillatort integral, singularity, Levin method, hybrid fuction

References

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