Gauss-Type Quadrature Rules Based on Identity-Type Functions
M. A. Bokhari (1), Asghar Qadir (1,2) ((1)Dept of Math & Stat,, KFUPM, Dhahran, Saudi Arabia, (2)CAMP, NUST, Rawalpindi, Pakistan)
TL;DR
This paper investigates Gauss-type quadrature rules over [0, 1] that incorporate function values and derivatives at the endpoints, aiming to improve numerical integration accuracy.
Contribution
It introduces new Gauss-type quadrature rules based on identity-type functions that utilize endpoint derivatives and values for enhanced integration.
Findings
Developed quadrature rules involving endpoint derivatives
Analyzed the accuracy and convergence of the rules
Provided numerical examples demonstrating effectiveness
Abstract
Some Gauss-type quadrature rules over [0, 1], which involve values and/or the derivative of the integrand at 0 and/or 1, are investigated
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Taxonomy
TopicsMathematical functions and polynomials · Iterative Methods for Nonlinear Equations · Mathematical Approximation and Integration