A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints
DOI10.1137/22m1494877arXiv2205.00516OpenAlexW4388705093MaRDI QIDQ6091099
Diego del-Castillo-Negrete, Minglei Yang, Guannan Zhang, Yanzhao Cao
Publication date: 24 November 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.00516
transportstochastic differential equationBrownian motionFeynman-Kac formulaexit timecompound Poisson processNonlocal diffusion equations
Analysis of algorithms and problem complexity (68Q25) Diffusion processes (60J60) Numerical solutions to stochastic differential and integral equations (65C30) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)
Cites Work
- Unnamed Item
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- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- A new approach for shape preserving interpolating curves
- Adapted solution of a backward stochastic differential equation
- Continuous and discontinuous finite element methods for a peridynamics model of mechanics
- Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions
- Numerical solution of stochastic differential equations with jumps in finance
- Numerical methods for the solution of partial differential equations of fractional order.
- Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion
- Weak approximation of killed diffusion using Euler schemes.
- Finite difference approximations for fractional advection-dispersion flow equations
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Reformulation of elasticity theory for discontinuities and long-range forces
- Numerical methods for a class of nonlocal diffusion problems with the use of backward SDEs
- A Feynman-Kac based numerical method for the exit time probability of a class of transport problems
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients
- Nonlocal convection-diffusion volume-constrained problems and jump processes
- Discrete-time approximation of decoupled Forward-Backward SDE with jumps
- Results on Nonlocal Boundary Value Problems
- Backward stochastic differential equations and integral-partial differential equations
- A speculative study of 2∕3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures
- Regularity theory for fully nonlinear integro-differential equations
- Time Discrete Taylor Approximations for It?? Processes with Jump Component
- Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- Convolution quadrature for the wave equation with a nonlinear impedance boundary condition
- A First-Order Numerical Scheme for Forward-Backward Stochastic Differential Equations in Bounded Domains
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion
- Image Denoising Methods. A New Nonlocal Principle
- Numerical methods for nonlocal and fractional models
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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