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arXiv · 2608.01932

Numerical approximation of fractional diffusion equations on metric graphs

David Bolin·Lenin Riera-Segura·Alexandre B. Simas
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Abstract

We study fractional diffusion equations on compact metric graphs, where the nonlocal dynamics is governed by fractional powers of the shifted Kirchhoff-Laplacian. Building on recent advances in the analysis of fractional operators on metric graphs, we establish a rigorous mathematical framework and propose a fully discrete scheme based on backward Euler time-stepping and finite element discretization. To approximate the action of the fractional operator, we employ rational approximations, reducing the problem to a sequence of sparse elliptic solves for efficient implementation. We derive error estimates for the temporal, spatial, and rational discretizations, and confirm convergence through numerical experiments.

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David Bolin, Lenin Riera-Segura, Alexandre B. Simas. 2026-08-03. Numerical approximation of fractional diffusion equations on metric graphs. https://arxiv.org/abs/2608.01932

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