@Article{IJNAM-18-1,
author = {Guang-Hua, Gao and Tang, Rui and Yang, Qian},
title = {A Compact Finite Difference Scheme for the Fourth-Order Time Multi-Term Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {1},
pages = {100--119},
abstract = {<p style="text-align: justify;">In this paper, a finite difference scheme is established for solving the fourth-order time
multi-term fractional sub-diffusion equations with the first Dirichlet boundary conditions. Using
the method of order reduction, the original problem is equivalent to a lower-order system. Then
the system is considered at some particular points, and the first Dirichlet boundary conditions
are also specially handled, so that the global convergence of the presented difference scheme
reaches $O(τ^2 + h^4)$, with $τ$ and $h$ the temporal and spatial step size, respectively. The energy
method is used to give the theoretical analysis on the stability and convergence of the difference
scheme, where some novel techniques have been applied due to the non-local property of fractional
operators and the numerical treatment of the first Dirichlet boundary conditions. Numerical
experiments further validate the theoretical results.</p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-18623},
url = {https://global-sci.com/article/82971/a-compact-finite-difference-scheme-for-the-fourth-order-time-multi-term-fractional-sub-diffusion-equations-with-the-first-dirichlet-boundary-conditions}
}