Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data (Q785560)

Backward fractional Feynman-Kac equation describes the functional distribution of the anomalous diffusion process. The time-space coupled fractional substantial derivative causes regularity problems. In this paper, the regularity requirement of the initial condition is weakened and optimal convergence rates are obtained. The Riemann-Liouville fractional substantial derivative is approximated by backward Euler and second-order backward difference convolution quadratures. Four numerical examples validate the predicted convergence rate in time and space and effectiveness of the proposed scheme.