Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem

DOI10.4208/nmtma.OA-2021-0173MaRDI QIDQ5094724

Jing Sun, Daxin Nie, Weihua Deng

Publication date: 4 August 2022

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.11378

zbMATH Keywords

error estimatesLagrange interpolationoperator splittingfinite differenceinhomogeneous fractional Dirichlet problemone- and two-dimensional integral fractional Laplacian

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• A new difference scheme for the time fractional diffusion equation
• A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
• Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
• What is the fractional Laplacian? A comparative review with new results
• Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes
• Fractional calculus for power functions and eigenvalues of the fractional Laplacian
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises
• Nonlinear Diffusion with Fractional Laplacian Operators
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• A Direct Approach to the Exit Problem
• Lévy Processes and Stochastic Calculus
• Iterative Solution Methods
• Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
• Boundary Problems for the Fractional and Tempered Fractional Operators
• Matrix Preconditioning Techniques and Applications
• Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian
• Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
• Finite Difference Schemes for the Tempered Fractional Laplacian
• Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
• A class of second order difference approximations for solving space fractional diffusion equations
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations

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