Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian

DOI10.1007/S10543-021-00860-5OpenAlexW3175106320MaRDI QIDQ2665553

Daxin Nie, Jing Sun, Weihua Deng

Publication date: 19 November 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.02349

zbMATH Keywords

error estimatebilinear interpolationthe weighted trapezoidal ruletwo-dimensional tempered fractional Laplacian

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Fractional partial differential equations (35R11) Numerical analysis (65-XX)

Related Items (7)

On the fractional Laplacian of some positive definite kernels with applications in numerically solving the surface quasi-geostrophic equation as a prominent fractional calculus model ⋮ Nonexistence of solutions to fractional parabolic problem with general nonlinearities ⋮ A Grid-Overlay Finite Difference Method for the Fractional Laplacian on Arbitrary Bounded Domains ⋮ An anisotropic tempered fractional \(p\)-Laplacian model involving logarithmic nonlinearity ⋮ Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes ⋮ Numerical approximations for the tempered fractional Laplacian: error analysis and applications ⋮ Asymptotic radial solution of parabolic tempered fractional Laplacian problem

Cites Work

• Unnamed Item
• Unnamed Item
• The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
• Ten equivalent definitions of the fractional Laplace operator
• Error bounds for polynomial tensor product interpolation
• Censored stable processes
• A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
• A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• The Fractional Laplacian
• Lévy Processes and Stochastic Calculus
• A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian
• Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise
• Boundary Problems for the Fractional and Tempered Fractional Operators
• Matrix Preconditioning Techniques and Applications
• Iterative Solution Methods
• Image Denoising Methods. A New Nonlocal Principle
• Finite Difference Schemes for the Tempered Fractional Laplacian
• Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
• The Mathematical Theory of Finite Element Methods
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian