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Volume 9, Issue 4
A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates

Guang-Hua Gao & Rui Liu

DOI: 10.4208/eajam.171118.060119

East Asian J. Appl. Math., 9 (2019), pp. 703-722.

Published online: 2019-10

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  • Abstract

A spatial compact difference scheme for a class of fourth-order temporal multi-term fractional wave equations is developed. The original problem is reduced to a lower order system and the corresponding time fractional derivatives are approximated by the $L$1-formula. The unconditional stability and convergence of the difference scheme are proved by the energy method. Numerical experiments support theoretical results.

  • Keywords

Compact difference scheme, multi-term fractional derivatives, spatial fourth-order derivative, stability, convergence.

  • AMS Subject Headings

65M06, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gaogh@njupt.edu.cn (Guang-Hua Gao)

976754568@qq.com (Rui Liu)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-9-703, author = {Gao , Guang-Hua and Liu , Rui}, title = {A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {703--722}, abstract = {

A spatial compact difference scheme for a class of fourth-order temporal multi-term fractional wave equations is developed. The original problem is reduced to a lower order system and the corresponding time fractional derivatives are approximated by the $L$1-formula. The unconditional stability and convergence of the difference scheme are proved by the energy method. Numerical experiments support theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.171118.060119}, url = {http://global-sci.org/intro/article_detail/eajam/13328.html} }
TY - JOUR T1 - A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates AU - Gao , Guang-Hua AU - Liu , Rui JO - East Asian Journal on Applied Mathematics VL - 4 SP - 703 EP - 722 PY - 2019 DA - 2019/10 SN - 9 DO - http://doi.org/10.4208/eajam.171118.060119 UR - https://global-sci.org/intro/article_detail/eajam/13328.html KW - Compact difference scheme, multi-term fractional derivatives, spatial fourth-order derivative, stability, convergence. AB -

A spatial compact difference scheme for a class of fourth-order temporal multi-term fractional wave equations is developed. The original problem is reduced to a lower order system and the corresponding time fractional derivatives are approximated by the $L$1-formula. The unconditional stability and convergence of the difference scheme are proved by the energy method. Numerical experiments support theoretical results.

Gao , Guang-Hua and Liu , Rui. (2019). A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates. East Asian Journal on Applied Mathematics. 9 (4). 703-722. doi:10.4208/eajam.171118.060119
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