International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

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Volume 8 Issue 2
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Computational Analysis of Integration Performance: Impact of Weight Functions and Node Distributions in Gaussian Quadrature

Author(s) Mr. Sidharth Ashok Tapare, Dr. Jaishree Saxena, Mrs. Mansi Shinde, Mrs. Nilam Ghadage
Country India
Abstract Gaussian quadrature is one of the most efficient techniques for high-accuracy numerical integration, due to its optimal node selection and weight computation based on orthogonal polynomials. Recent advances have focused on high-precision algorithms, generalized weight functions, and improved error estimation; however, a comprehensive computational evaluation of how weight functions and node distributions jointly affect integration performance remains limited. This paper presents a systematic computational analysis of classical and modified Gaussian quadrature schemes under varying weight formulations and node configurations. Nodes and weights are computed using stable high-relative-accuracy algorithms, and performance is assessed through error norms, convergence behavior, numerical stability indicators, and computational cost across smooth, oscillatory, and special-function integrals. The results demonstrate that integration accuracy depends strongly on the compatibility between the quadrature weight function and the integrand structure. Adaptive and modified weight strategies significantly enhance performance for non-standard integrals, while precise node computation improves robustness in high-order implementations. The findings establish quantitative relationships between node distribution characteristics and error decay, providing practical guidelines for selecting and designing efficient Gaussian quadrature schemes in advanced scientific computing applications.
Keywords Gaussian Quadrature, Weight Functions, Quadrature Nodes, Orthogonal Polynomials, High-Order Computational Methods
Field Mathematics
Published In Volume 8, Issue 2, March-April 2026
Published On 2026-04-08
DOI https://doi.org/10.36948/ijfmr.2026.v08i02.73922
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E-ISSN 2582-2160
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