English

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations

Numerical Analysis 2025-06-25 v1 Numerical Analysis

Abstract

In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal error estimates of stochastic convergence not only balance discretization errors, the noise, and the number of observation points, but also propose an a priori choice of regularization parameters. Finally, several numerical experiments are presented to demonstrate the efficiency and accuracy of the algorithm.

Keywords

Cite

@article{arxiv.2506.18948,
  title  = {Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations},
  author = {Dakang Cen and Zhiyuan Li and Wenlong Zhang},
  journal= {arXiv preprint arXiv:2506.18948},
  year   = {2025}
}

Comments

27 pages. arXiv admin note: text overlap with arXiv:2506.17575