Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates  

作　　者：Guang-hua Gao Biao Ge Zhi-Zhong Sun 

机构地区：[1]College of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,P.R.China [2]School of Mathematics,Southeast University,Nanjing 211189,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第3期634-667,共34页高等学校计算数学学报（英文版）

基　　金：supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20191375);the project NUPTSF(No.NY220037).

摘　　要：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 secondorder 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.

关 键 词：Fisher equation linearized difference scheme SOLVABILITY convergence CONSERVATION 

分 类 号：O17[理学—数学]