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Volume 9, Issue 4
A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations

Jinhong Jia & Hong Wang

DOI: 10.4208/eajam.271118.280319

East Asian J. Appl. Math., 9 (2019), pp. 755-779.

Published online: 2019-10

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  • Abstract

In this work, we consider a boundary value problem involving Caputo derivatives defined in the plane. We develop a fast locally refined finite volume method for variable-coefficient conservative space-fractional diffusion equations in the plane to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

  • Keywords

Space-fractional diffusion equation, locally refined mesh, Toeplitz matrix, circulant matrix, finite volume method.

  • AMS Subject Headings

34A08, 65F10, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jhjia@sdnu.edu.cn (Jinhong Jia)

hwang@math.sc.edu (Hong Wang)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-9-755, author = {Jia , Jinhong and Wang , Hong}, title = {A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {755--779}, abstract = {

In this work, we consider a boundary value problem involving Caputo derivatives defined in the plane. We develop a fast locally refined finite volume method for variable-coefficient conservative space-fractional diffusion equations in the plane to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.271118.280319}, url = {http://global-sci.org/intro/article_detail/eajam/13331.html} }
TY - JOUR T1 - A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations AU - Jia , Jinhong AU - Wang , Hong JO - East Asian Journal on Applied Mathematics VL - 4 SP - 755 EP - 779 PY - 2019 DA - 2019/10 SN - 9 DO - http://doi.org/10.4208/eajam.271118.280319 UR - https://global-sci.org/intro/article_detail/eajam/13331.html KW - Space-fractional diffusion equation, locally refined mesh, Toeplitz matrix, circulant matrix, finite volume method. AB -

In this work, we consider a boundary value problem involving Caputo derivatives defined in the plane. We develop a fast locally refined finite volume method for variable-coefficient conservative space-fractional diffusion equations in the plane to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.

Jia , Jinhong and Wang , Hong. (2019). A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations. East Asian Journal on Applied Mathematics. 9 (4). 755-779. doi:10.4208/eajam.271118.280319
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