Numerical Method to Modify the Fractional‐Order Diffusion Equation

Yunkun Chen

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

Abstract: Time or space or time‐space fractional‐order diffusion equations (FODEs) are widely used to describe anomalous diffusion processes in many physical and biological systems. In recent years, many authors have proposed different numerical methods to solve the modified fractional‐order diffusion equations, and some achievements have been obtained. However, to our knowledge of the literature, up to date, all the proposed numerical methods to modify FODE have achieved at most a second‐order time accuracy. In this study, we focus mainly on the numerical methods based on numerical integration in order to modify the fractional‐order diffusion equation: 1+1/12δx2pjk−1+1/12δx2pjk−1=μα∑l=0kλαlδx2pjk−l+ μβ∑l=0kλβlδx2pjk−l+τ/21+1/12δx2fjk−1+fjk, k=1,21,210,1,…,K;j=,…,j−,pj0=ωj,j=,…,J, p0k=φtk,pjk=ψtk,k=0,1,…,K,fjl=fxj,tl,ωj=ωxj. Accordingly, numerical methods can be built to modify FODE with second‐order time accuracy and fourth‐order spatial accuracy in (∂p(x, t)/∂t) = ((∂1−α/∂t1−α) + B(∂1−β/∂t1−β))(∂2p(x, t)/∂x2) + f(x, t), 0

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2022/4846747

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:4846747

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().