3 papers
math.NA2026
An Exact-Moment Local Legendre Frame Method with Block Convolution for Caputo Fractional Differentiation
Zhenyu Zhao, Benxue Gong, Tinggang Zhao +1
We propose a local Legendre frame method for the accurate computation of Caputo fractional derivatives of order \(0<α<1\). On each local subinterval, the function is represented by…
math.NA2026
Local Legendre Frame Approximation from Equispaced Data
Benxue Gong, Zhenyu Zhao, Chenyang Wang
We propose a local Legendre frame (LLF) method for function approximation from equispaced data on a finite interval. Motivated by the difficulty of stable high-order polynomial app…
math.NA2026
High-precision quadrature via local Fourier extension: analytic integration, uniform sampling, and correction for piecewise smooth integrands
Xinran Liu, Zhenyu Zhao, Benxue Gong
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabil…