High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth data

The Feynman-Kac equation governs the distribution of statistical observable — functional, having wide applications in almost all disciplines. After overcoming some challenges from time-space coupled nonlocal operator and possible low regularity this paper develops high-order fully discrete scheme for backward fractional by using difference formulas (BDF) convolution quadrature time, finite element method space, correction terms. With a systematic correction, high convergence order is achieved up to 6 without deteriorating optimal space requirement on solution. Finally, extensive numerical experiments validate effectiveness schemes.