Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates
Year: 2023
Author: Biao Ge, Zhi-Zhong Sun, Guang-Hua Gao, Biao Ge, Zhi-Zhong Sun
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 634–667
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0123
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 634–667
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Fisher equation linearized difference scheme solvability convergence conservation.