Numerical integration for Muntz polynomial and Muntz logarithmic polynomial

Sunita Kumari Nayak; Saumya Ranjan Jena; Prabhat Kumar Rout; Arjun Kumar Paul

Sunita Kumari Nayak School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar-751024.
Saumya Ranjan Jena School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar-751024.
Prabhat Kumar Rout School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar-751024.
Arjun Kumar Paul School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar-751024.

Abstract

In this manuscript, a higher precision rule is constructed for the numerical evaluation Muntz and Muntz logarithmic polynomials.Here the transformation have been taken from $0\leq x\leq1$ to $-1\leq x\leq1$ by using monomial transformations. The mixed quadrature rule and the singularities are extracted by taking the linear combination two individual quadrature rules . The efficiency and accuracy of the present rule and error bound are fully tested on numerical problems.