Error estimates of implicit-explicit compact BDF2 schemes for the pseudo parabolic equations with logarithmic nonlinearity

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-23 DOI:10.1016/j.apnum.2025.01.010

Qifeng Zhang , Haiyan Cao , Hongyu Qin

引用次数: 0

Abstract

In this paper, two classes of linearized difference schemes are presented for the one and two-dimensional pseudo parabolic equations with logarithmic nonlinearity. These schemes are derived based on the implicit-explicit second-order backward differential formula (BDF2) for the temporal discretization and fourth-order compact/second-order difference schemes for spatial discretization. With the help of the truncation function method and regularization technique, error estimates for the logarithmic nonlinear term are handled rigorously. As a result, the convergence of the fully-discrete schemes is obtained based on the energy argument. Extensive numerical examples are presented to confirm the theoretical results.

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对数非线性伪抛物方程隐显紧BDF2格式的误差估计

本文给出了具有对数非线性的一维和二维伪抛物型方程的两类线性化差分格式。这些格式是基于时间离散化的隐式-显式二阶后向微分公式（BDF2）和空间离散化的四阶紧凑/二阶差分格式导出的。利用截断函数法和正则化技术，对对数非线性项进行了严格的误差估计。结果表明，基于能量参数得到了全离散格式的收敛性。通过大量的数值算例验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.