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Enhancing Interpolation and Approximation Error Estimates Using a Novel Taylor-like Formula (2310.19483v1)
Published 30 Oct 2023 in math.NA and cs.NA
Abstract: In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error estimate. Following the same principles, we also develop a novel numerical scheme for the heat equation that yields a better error estimate compared to the classical implicit finite differences scheme.