2025/01/24 by Samala Rathan, Mahata, Shipra, Rathan, Samala +4
Computer Science · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2501.14608
openalex publication_date 2025/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when the position of an isolated discontinuity in the function and the jump in the function and its derivatives at that position are known. Traditional numerical integration rules are exact for polynomials of certain degree. However, they may not provide accurate results for piece-wise polynomials or functions with discontinuities without modifying the location and number of data points in the formula. Our proposed correction terms address this limitation, enabling the integration rule to conserve its accuracy even in the presence of a jump discontinuity. The numerical experiments that we present support the theoretical results obtained.