Research articles
ScienceAsia 49 (2023):ID 693-702 |doi:
10.2306/scienceasia1513-1874.2023.048
A sixth-order finite difference method for solving the
generalized Burgers-Fisher and generalized Burgers-Huxley
equations
Sheng-en Liu, Yongbin Ge*, Fang Tian
ABSTRACT: The generalized Burgers-Huxley and generalized Burgers-Fisher equations are solved by using a new sixthorder finite difference method. Such equations are discretized in space by a five-point sixth-order finite difference
scheme combined with a truncation error modification technique and in time by the sixth-order backward difference
formula, which constitutes a finite difference scheme with the sixth-order accuracy in both space and time. Then, the
Crank-Nicolson method combined with the Richardson extrapolation technique is employed to obtain the approximate
solutions at the starting time steps which can keep the spatio-temporal sixth-order accuracy of the main scheme. The
linear system formed by this scheme at each time step is efficiently solved by the Thomas algorithm. Finally, some
numerical experiments are carried out to verify the accuracy and reliability of the proposed method.
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Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan 750021 China |
* Corresponding author, E-mail: gybnxu@yeah.net
Received 10 Sep 2022, Accepted 29 Apr 2023
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