A Weighted ADI Scheme for Subdiffusion Equations

A weighted ADI scheme is proposed for solving two-dimensional anomalous diffusion equations with the fractional Caputo derivative. The Alikhanov formula (J Comput Phys 280:424–438, 2015 ) with a weaker assumption is applied to approximate the fractional derivative and a high-order perturbed term of...

Full description

Saved in:
Bibliographic Details
Published in:Journal of scientific computing 2016-12, Vol.69 (3), p.1144-1164
Main Authors: Liao, Hong-lin, Zhao, Ying, Teng, Xing-hu
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Energy methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Smoothness
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A weighted ADI scheme is proposed for solving two-dimensional anomalous diffusion equations with the fractional Caputo derivative. The Alikhanov formula (J Comput Phys 280:424–438, 2015 ) with a weaker assumption is applied to approximate the fractional derivative and a high-order perturbed term of temporal order 1 + 2 α is added to the pure implicit approach. By using the discrete energy method, it is proven that the ADI scheme is stable and convergent with the temporal order of min { 1 + 2 α , 2 } such that it achieves second-order time accuracy when 1 2 ≤ α < 1 . Numerical experiments are included to support the theoretical analysis. Application of suggested method to the solution which lacks the smoothness near the initial time is examined by employing a class of nonuniform meshes refined near the singular point.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-016-0230-9