Numerical Analysis of Scattered Point Measurement-Based Regularization for Backward Problems for Fractional Wave Equations

Source abstract

In this work, our aim is to reconstruct the unknown initial value in a fractional wave system from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under low-regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal stochastic convergence error estimates balance discretization errors, noise, and the number of observation points and also provide a basis for an a priori choice of regularization parameters. Finally, several numerical experiments are presented to demonstrate the efficiency and accuracy of the algorithm.