1. SWAGATIKA DAS - Research Scholar, Biju Patanaik University and Technology, Chhend Colony, Rourkella, Odisha, India.
2. GEETANJALI PRADHAN - Department of Mathematics & Humanities, Odisha University of Technology and Research Bhubaneswar,
Odisha, India.
3. RABINDRA NATH DAS - Department of Mathematics and Computer Science, Gangadhar Meher (Autonomous) College, Sambalpur,
Odisha, India.
Some quadrature rules of a degree of precision six, eight, and ten have been formulated for numerical evaluation of complex Cauchy principal value integrals and their asymptotic errors have been obtained. The rules which have been constructed in this paper involve neither the derivative nor its approximation at any of the nodes on which the rules are based. Besides, a few more quadrature rules from the rules derived in the first instant have also been constructed following the technique of extrapolation and their asymptotic error estimates have also been obtained. Some standard test integrals of the Cauchy principal value type and Hyper singular type have been numerically evaluated by each of the rules constructed in this paper.
Asymptotic error, Cauchy principal value, degree of precision, error bound, error constant, Hadamard finite part-integral (HFP), hyper singular.