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This is a Quantitative Study study (also classified as: Experimental Study).

October 2, 2025Open Access

Discrete Differential Principle for Continuous Smooth Function Representation

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Proposed method demonstrates tight error bounds for derivatives in fluid mechanics and visual perception.

The proposed discrete differential operator achieves high-order accuracy in estimating derivatives.
Error propagation is significantly mitigated during derivative computation with the new method.
Rigorous error bounds show improved estimates for lower-order derivatives within function representation.
The two-dimensional extension of the method enables effective multivariate derivative calculations.

Wang et al. (2025) studied this question.

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