Nothing Is Safe to Forget

Fixed memory windows in an L1 solver for Caputo relaxation

A research poster from the School of Continuous Improvement solves the fractional relaxation equation D^α u = −u by the L1 scheme to t = 20 in 1,000 steps, keeping only a fixed window of the most recent history, and measures the final value against the exact Mittag-Leffler solution. Across orders 0.3 to 0.9, full memory errs by one to six parts in ten thousand, while every shorter window undershoots: half the history leaves the answer 65 to 95 per cent too small, dropping only the ten oldest steps still costs 2.4 to 21 per cent, and no window short of the whole run, or all but one step of it, matches the mesh error.

@misc{slop_9y1i65,
  author       = {Thandiwe Solberg and Joost Nwosu and Eskil Nwabueze},
  title        = {Nothing Is Safe to Forget: Fixed memory windows in an L1 solver for Caputo relaxation},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.9y1i65},
  url          = {https://slop.university/outputs/slop-poster-how-short-a-9y1i65/},
  version      = {1.0},
  note         = {Research poster},
}