Numerical algorithms for the forward and backward fractional Feynman-Kac equations

DOI10.1007/s10915-014-9873-6zbMath1335.65069arXiv1401.0654OpenAlexW1990217702MaRDI QIDQ2355555

Weihua Deng, Eli Barkai, Minghua Chen

Publication date: 24 July 2015

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0654

zbMATH Keywords

convergencefinite elementSchrödinger equationnumerical stabilityfinite differencenumerical experimentfractional substantial derivativefractional Feynman-Kac equationoptimal convergence ordernumerical inversion of Laplace transforms

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Laplace transform (44A10) Numerical methods for integral transforms (65R10) Fractional partial differential equations (35R11)

Related Items (23)

Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative ⋮ High order schemes for the tempered fractional diffusion equations ⋮ Numerical algorithms for the time-space tempered fractional Fokker-Planck equation ⋮ A second-order difference scheme for the time fractional substantial diffusion equation ⋮ Tempered fractional order compartment models and applications in biology ⋮ Numerical approaches to the functional distribution of anomalous diffusion with both traps and flights ⋮ High order algorithm for the time-tempered fractional Feynman-Kac equation ⋮ A numerical algorithm for the Caputo tempered fractional advection-diffusion equation ⋮ Superconvergence analysis of anisotropic finite element method for the time fractional substantial diffusion equation with smooth and nonsmooth solutions ⋮ An exponential B-spline collocation method for the fractional sub-diffusion equation ⋮ Correction of high-order BDF convolution quadrature for fractional Feynman-Kac equation with Lévy flight ⋮ Unnamed Item ⋮ Numerical schemes of the time tempered fractional Feynman-Kac equation ⋮ Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman-Kac equation ⋮ An implicit Keller box numerical scheme for the solution of fractional subdiffusion equations ⋮ Local discontinuous Galerkin methods for the time tempered fractional diffusion equation ⋮ Two \(L1\) schemes on graded meshes for fractional Feynman-Kac equation ⋮ A high-order algorithm for time-Caputo-tempered partial differential equation with Riesz derivatives in two spatial dimensions ⋮ The asymptotic behaviour of fractional lattice systems with variable delay ⋮ Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data ⋮ Discretized fractional substantial calculus ⋮ Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes ⋮ High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights

Uses Software

• FODE

Cites Work

• Unnamed Item
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