一类拟变量网格高分辨率紧凑算子格式的Burger - huxley和Burger - fisher方程

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2020-11-03 DOI:10.5206/mase/10837
Navnit Jha, Madhav Wagley
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引用次数: 1

摘要

我们描述了一种准变网格隐式紧致有限差分离散化,该离散化在空间方向上具有四阶精度,在时间方向上具有二阶精度,用于获得广义Burger’s-Huxley和Burger’s Fisher方程的数值解值。对于拟变网格网络上的一般一维拟线性抛物型偏微分方程,在均匀网格网络情况下,高阶紧致格式的局部截断误差大小不变的情况下,导出了新的差分格式。在实际应用中,与同等大小的均匀网格高阶格式相比,准变网格高阶紧致格式能得到更精确的解。对新方案进行了详细的阐述,并讨论了基于傅立叶分析的稳定性理论。利用拟变网格高阶紧致格式得到了广义Burger’s Huxley方程和Burger’s-Fisher方程的计算结果,并与均匀网格高阶格式的数值解进行了比较,以证明其计算能力和精度。
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A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation
We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy.
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来源期刊
CiteScore
1.40
自引率
0.00%
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审稿时长
21 weeks
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