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Research articles

ScienceAsia 49 (2023): 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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a 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