4.6 Article

Finite difference discretization for one-dimensional higher-order integral fractional Laplacian and its application

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

HIGHLY ACCURATE OPERATOR FACTORIZATION METHODS FOR THE INTEGRAL FRACTIONAL LAPLACIAN AND ITS GENERALIZATION

Yixuan Wu et al.

Summary: In this paper, a new class of operator factorization methods is proposed for discretizing the integral fractional Laplacian. The method allows for easily increasing numerical accuracy and maintains its scheme structure and computer implementation. Numerical experiments demonstrate the method's efficiency in approximating the fractional Laplacian and solving the fractional Poisson problems.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2022)

Article Computer Science, Interdisciplinary Applications

Fractional centered difference scheme for high-dimensional integral fractional Laplacian

Zhaopeng Hao et al.

Summary: This study introduces a finite difference method for solving the fractional diffusion equation and analyzes its stability and convergence. It also presents a fast solver and provides numerical results to support the theoretical findings.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Computer Science, Interdisciplinary Applications

A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem

Siwei Duo et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Article Mathematics, Applied

ON THE LOSS OF MAXIMUM PRINCIPLES FOR HIGHER-ORDER FRACTIONAL LAPLACIANS

Nicola Abatangelo et al.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2018)

Article Mathematics, Interdisciplinary Applications

Numerical methods for fractional diffusion

Andrea Bonito et al.

COMPUTING AND VISUALIZATION IN SCIENCE (2018)

Article Mathematics, Applied

A Class of High Order Nonlocal Operators

Xiaochuan Tian et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2016)

Article Mathematics, Applied

LOCAL INTEGRATION BY PARTS AND POHOZAEV IDENTITIES FOR HIGHER ORDER FRACTIONAL LAPLACIANS

Xavier Ros-Oton et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2015)

Article Mathematics, Applied

The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary

Xavier Ros-Oton et al.

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES (2014)

Article Mathematics, Applied

NUMERICAL METHODS FOR THE FRACTIONAL LAPLACIAN: A FINITE DIFFERENCE-QUADRATURE APPROACH

Yanghong Huang et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2014)