2019/11/02 by Yaming Chen, Chen, Yaming, Xiaogang Deng +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Computational Physics (physics.comp-ph) #Computer science #Convergence (economics) #Economics #FOS: Physical sciences #Finite difference scheme #Fokker–Planck equation #Mathematical analysis #Mathematics #Order (exchange) #Partial differential equation #Physics #Rate of convergence #Scheme (mathematics) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Stochastic processes and financial applications #cond-mat.stat-mech #physics.comp-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1911.00633
published in arXiv (Cornell University) (Cornell University)
arxiv created 2019/11/02 · arxiv updated 2019/11/05
Recently a useful finite-difference scheme was proposed in [Phys. Rev. E 98, 033302 (2018)] to solve Fokker-Planck equations with drift-admitting jumps. However, while the scheme is fifth order for the case with smooth drifts, it is only second order for the case with discontinuous drifts. To rectify this, we propose in this paper an improved scheme that achieves a fifth-order convergence rate for the case with drift-admitting jumps. Numerical experiments are also employed to verify the validity of the scheme.