Convolution Quadrature with Adaptive History Compression for Variable-Order Fractional Reaction--Diffusion Equations
Year: 2026
Type: preprint
Abstract: We develop a fully implicit fast method for semilinear variable-order fractional reaction--diffusion equations with periodic fractional diffusion and exponential-transition Scarpi memory. A Volterra-resolvent analysis establishes local well-posedness and temporal regularity estimates that describe the weak initial singularity. Backward Euler convolution quadrature combined with Fourier pseudospectral discretization achieves mesh-uniform stability and positive-time first-order convergence. To accelerate the scheme, we utilize Cauchy--FFT weight recovery and adaptive blockwise sum-of-exponentials compression, which significantly reduces the cost of history evaluation under local error control. A logarithmic perturbation bound quantifies the effects of weight recovery, history compression, and inexact nonlinear solves, giving tolerance conditions that preserve the convergence order. Numerical experiments confirm the first-order accuracy and demonstrate that the accelerated method efficiently resolves long-time spatial patterns at a substantially reduced computational cost.
Source: arXiv (Cornell University)
Authors: Yuan, Pu, Zegeling, Paul
Institution: Utrecht University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223104301