On extrapolatory mixed quadrature rule for approximate evaluation of real definite integrals

Saumya Ranjan Jena; Sunita Kumari Nayak; Itishree Sahu; Prasanta Kumar Mohanty

Saumya Ranjan Jena Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Odisha, Bhubaneswar-751024.
Sunita Kumari Nayak Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Odisha, Bhubaneswar-751024
Itishree Sahu Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Odisha, Bhubaneswar-751024
Prasanta Kumar Mohanty Department of Mathematics, School of Applied Sciences, KIIT Deemed to be University, Odisha, Bhubaneswar-751024

Abstract

This study employs Richardson extrapolation on mixed quadrature rule which is imbraided by Lobatto-4-point rule $(R_{L4}(f))$ with Gauss-Legendre-3-point rule $(R_{GL3}(f))$ to form the extrapolatory quadrature rule $(R_{RL4GL3} (f))$ of precision nine. The current rule is numerically verified with six test problems and the bound for the error is resolved with suitable examples.