数学
离散化
点式的
伯格斯方程
紧致有限差分
数学分析
操作员(生物学)
准确度顺序
有限差分法
应用数学
有限差分
偏微分方程
特征线法
基因
抑制因子
化学
转录因子
生物化学
作者
Tao Guo,Mahmoud A. Zaky,Ahmed S. Hendy,Wenlin Qiu
标识
DOI:10.1016/j.apnum.2022.11.023
摘要
This paper formulates a third-order backward differentiation formula (BDF3) fourth-order compact difference scheme based on a developed fourth-order operator for computing the approximate solution of the Burger's equation. The equation is one of the useful description for modeling nonlinear acoustics, gas dynamics, fluid mechanics and etc. This proposed approach approximates the solution of Burger's equation with the help of two main steps. In the first step, the temporal discretization is accomplished by virtue of the BDF3 approach. In the second step, a developed fourth-order operator and the classic compact difference formula combine with the method of order reduction are applied for spatial discretization, thereby constructing a fully-discrete scheme. The theoretical analysis is proved in detail by means of the discrete energy method. The proposed scheme is convergent with third order for time and fourth order for space. Numerical results are carried out to verify the validity and accuracy of the proposed method.
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