Caputo导数的非均匀L1-2公式及其应用

doi:10.12066/j.issn.1007-2861.2658

Abstract

Abstract: This paper constructs a numerical approximation formula for the Caputo derivative of order α∈(0，1). Considering the weak regularity of the Caputo derivative at the initial time, linear interpolation is employed over the first subinterval of the non-uniform mesh, while quadratic interpolation is utilized for each subsequent subinterval, leading to the derivation of a non-uniform L1-2 formula. It is proven that the truncation error can achieve (3-fi)-order accuracy, and the corresponding coefficient properties are discussed. The derived formula is applied to the numerical solution of the time-fractional diffusion equation, and numerical experiments have verified the effectiveness and correctness of the formula.

Key words: L1-2 formula, graded mesh, weak regularity, fractional diffusion equation

CLC Number:

O241.82

WANG Junling, LI Dongxia. The non-uniform L1-2 formula for Caputo derivatives and its applications[J]. Journal of Shanghai University（Natural Science Edition）, 2026, 32(1): 166-186.

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The non-uniform L1-2 formula for Caputo derivatives and its applications

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