Study of some anti Newtonian and anti non Newtonian quadrature with special reference to mixed and mean quadrature

Abstract

he thesis titled Study of Some Anti-Newtonian and Anti-Non-Newtonian Quadrature with Special Reference to Mixed and Mean Quadrature comprises seven chapters. newlineThe first chapter, Introduction provides a historical overview of numerical analysis as a fundamental area of mathematics. It then introduces quadrature rules, which are employed for the numerical evaluation of definite integrals, and explores their applications to Fredholm integral equations. newlineIn the second chapter, titled Methodology , we provide an in-depth exploration of several fundamental quadrature rules. This includes deriving and examining the Newton-Cotes rules, various non-Newtonian Gaussian quadrature methods, and Lobatto rules. We discuss the error estimates associated with each of these techniques and evaluate their computational efficacy. Furthermore, the chapter extends to the application of these quadrature methods in solving Fredholm integral equations, demonstrating their relevance and effectiveness in this context. This comprehensive analysis aims to elucidate the theoretical foundations and practical implications of these quadrature techniques in numerical integration. newlineIn the third chapter, titled Review of Literature , we investigate various methods employed by researchers to calculate areas under curves. These methods are crucial for accurate computations, and this review aims to offer a clear overview of their applications. We also examine how researchers are developing specialized techniques to address challenging scena newline