Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation-Reference-Cited by-同舟云学术

Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation

Published:2023-10-11 Issue:10 Volume:12 Page:959
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Wu Fangfang¹^ORCID,Lu Chuangui¹,Wang Yingying¹,Hu Na¹

Affiliation:

1. College of Science, Shenyang University of Technology, Shenyang 110870, China

Abstract

This paper is concerned with the lattice Boltzmann (LB) method for a class of time fractional partial differential equations (FPDEs) in the Caputo sense. By utilizing the properties of the Caputo derivative and discretization in time, FPDEs can be approximately transformed into standard partial differential equations with integer orders. Through incorporating an auxiliary distribution function into the evolution equation, which assists in recovering the macroscopic quantity u, the LB model with spatial second-order accuracy is constructed. The numerical experiments verify that the numerical results are in good agreement with analytical solutions and that the accuracy of the present model is better than the previous solutions.

Funder

National Natural Science Foundation of China

education department project of Liaoning Province

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/959/pdf

Reference43 articles.

1. Podlubnv, I. (1999). Fractional Differential Equations, Academic Press.

2. Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation;An;Appl. Math. Comput.,2019

3. Long memory processes and fractional integration in econometrics;Baillie;J. Econom.,1996

4. Diethelm, K., and Ford, N.J. (2010). The Analysis of Fractional Differential Equations, Springer. Lecture Notes in Mathematics.

5. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier.