@Article{NMTMA-16-3,
author = {Ge, Biao and Zhi-Zhong, Sun and Guang-Hua, Gao and Ge, Biao and Zhi-Zhong, Sun},
title = {Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {3},
pages = {634--667},
abstract = {<p style="text-align: justify;">A three-level linearized difference scheme for solving the Fisher equation
is firstly proposed in this work. It has the good property of discrete conservative
energy. By the discrete energy analysis and mathematical induction method, it is
proved to be uniquely solvable and unconditionally convergent with the second-order accuracy in both time and space. Then another three-level linearized compact difference scheme is derived along with its discrete energy conservation law,
unique solvability and unconditional convergence of order two in time and four in
space. The resultant schemes preserve the maximum bound principle. The analysis
techniques for convergence used in this paper also work for the Euler scheme, the
Crank-Nicolson scheme and others. Numerical experiments are carried out to verify
the computational efficiency, conservative law and the maximum bound principle of
the proposed difference schemes.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0123},
url = {https://global-sci.com/article/90222/conservative-three-level-linearized-finite-difference-schemes-for-the-fisher-equation-and-its-maximum-error-estimates}
}