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04/16/2023
The Contour integral method for Feynman-Kac equation with two internal states
We develop the contour integral method for numerically solving the Feynm...
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02/06/2023
Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution
Finite difference method as a popular numerical method has been widely u...
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10/18/2022
Analyses of the contour integral method for time fractional subdiffusion-normal transport equation
In this work, we theoretically and numerically discuss the time fraction...
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09/02/2022
Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise
Super- and sub- diffusions are two typical types of anomalous diffusions...
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05/31/2022
A sharp α-robust L1 scheme on graded meshes for two-dimensional time tempered fractional Fokker-Planck equation
In this paper, we are concerned with the numerical solution for the two-...
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05/31/2022
Local discontinuous Galerkin method for the Backward Feynman-Kac Equation
Anomalous diffusions are ubiquitous in nature, whose functional distribu...
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05/23/2022
Numerical method for the Fokker-Planck equation of Brownian motion subordinated by inverse tempered stable subordinator with drift
In this work, based on the complete Bernstein function, we propose a gen...
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01/26/2022
Numerical Approximation for Stochastic Nonlinear Fractional Diffusion Equation Driven by Rough Noise
In this work, we are interested in building the fully discrete scheme fo...
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12/10/2021
Regularity theory and numerical algorithm for the fractional Klein-Kramers equation
Fractional Klein-Kramers equation can well describe subdiffusion in phas...
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09/07/2021
Numerical approximations for the fractional Fokker-Planck equation with two-scale diffusion
Fractional Fokker-Planck equation plays an important role in describing ...
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07/25/2021
Identifying the fragment structure of the organic compounds by deeply learning the original NMR data
We preprocess the raw NMR spectrum and extract key characteristic featur...
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06/02/2021
An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion
We study the inverse random source problem for the time-space fractional...
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04/28/2021
A unified convergence analysis for the fractional diffusion equation driven by fractional Gaussion noise with Hurst index H∈(0,1)
Here, we provide a unified framework for numerical analysis of stochasti...
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01/27/2021
Finite difference method for inhomogeneous fractional Dirichlet problem
We make the split of the integral fractional Laplacian as (-Δ)^s u=(-Δ)(...
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01/20/2021
Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian
In this paper, we provide a framework of designing the local discontinuo...
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01/06/2021
Numerical analysis for stochastic time-space fractional diffusion equation driven by fractional Gaussion noise
In this paper, we consider the strong convergence of the time-space frac...
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07/28/2020
Strong convergence order for the scheme of fractional diffusion equation driven by fractional Gaussion noise
Fractional Gaussian noise models the time series with long-range depende...
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07/06/2020
Higher order approximation for stochastic wave equation
The infinitesimal generator (fractional Laplacian) of a process obtained...
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06/29/2020
High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth data
The Feynman-Kac equation governs the distribution of the statistical obs...
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12/15/2019
Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise
This paper discusses the fractional diffusion equation forced by a tempe...
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11/16/2019
Galerkin finite element approximation for semilinear stochastic time-tempered fractional wave equations with multiplicative white noise and fractional Gaussian noise
To model wave propagation in inhomogeneous media with frequency-dependen...
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11/06/2019
Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data
In this paper, we are concerned with the numerical solution for the back...
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10/12/2019