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

    Guang-hua Gao, Biao Ge,Zhi-Zhong Sun

    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS（2023）

    Nanjing Univ Posts & Telecommun

    Cited 1|Views31
    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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    Key words
    Fisher equation,linearized difference scheme,solvability,convergence,conservation
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