Work

Efficient Numerical Algorithms for Three-Dimensional Fractional Partial Differential Equations

Year: 2014

Type: article

Abstract: This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation.The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative.We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions.In particular, for the Riesz fractional diffusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.

Source: Journal of Computational Mathematics

DOI: 10.4208/jcm.1401-m3893

Authors: Weihua Deng null, Minghua Chen

Institution: Lanzhou University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Program for New Century Excellent Talents in University, Fundamental Research Funds for the Central Universities