On the approximate evaluation of oscillatory-singular integrals

ABOUT THE AUTHORS M.K. Hota is presently working as a faculty in Mathematics, Nayagarh Autonomous College, Nayagarh, Odisha, India. His research interest includes issues related to Numerical Analysis, Artificial Neural Network (Nero-fuzzy system) and Graph Theory. He is reviewer of many international and national journals. His great deal of research studies published at different national and international journals as well as conference proceedings. A.K. Saha is an asst professor in Mathematics, Department of Education in Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, Odisha, India, is a research Scholar of the Department of Mathematics, School of Applied Science, KIIT University, Odisha of India. Presently, he is doing research on numerical quadrature rules for integrals of real and complex plane. PUBLIC INTEREST STATEMENT Integrals frequently appeared in sciences and engineering. In practice, we are confronted with different kinds of difficulties in evaluating integrals analytically. Thus, an alternating technique becomes absolutely necessary in order to evaluate, which has given birth to the technique of numerical integration or mechanical quadrature. In adopting this technique the exact value of the integral needs to be sacrificed and we have to be content with its approximate value. For this reason numerical integration is widely known as “Approximate integration”. Received: 25 October 2016 Accepted: 18 March 2017 First Published: 22 May 2017