Analysis Of The Stability And Convergence Of The Numerical Method For The Backward Fractional Feynman-Kac Equation

Using the Feynman path integral method,Kac has obtained the Schrodinger equation corresponding to the direction of the imaginary time,which is used to describe the distribution law of diffusional motion functionals.This is the Feynman-Kac equation,which has applications in physics.The backward fraction-al Feynman-Kac equation is proposed when studying the non-Brownian functional distribution and anomalous diffusion phenomenon,where the fractional material derivative introduced is a non-local space-time coupling operator.A high-precision discrete format of fractional material derivatives has been given in the literature,and a numerical method for solving the backward fractional Feynman-Kac equation has been constructed.This paper further validates the stability and convergence of numerical methods,and obtains theoretical analysis results of numerical stability and second-order convergence.The results of the numerical experiments show the correctness of the theoretical results.