线性和半线性抛物方程指数中点法的后验误差估计

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED Numerical Algorithms Pub Date : 2024-09-19 DOI:10.1007/s11075-024-01940-7

Xianfa Hu, Wansheng Wang, Mengli Mao, Jiliang Cao

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引用次数: 0

摘要

本文针对线性和半线性抛物线方程，建立了指数中点法时间离散化的后验误差估计。使用由节点值的连续分片线性插值定义的指数中点近似会产生次优阶次估计。基于整个函数的特性，我们引入了指数中点法的连续和片断二次时间重构，从而得出最优阶次估计值；误差边界完全取决于离散化参数、问题数据和整个函数的近似值。我们通过几个数值示例来说明理论结果。

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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A posteriori error estimates for the exponential midpoint method for linear and semilinear parabolic equations

In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are established for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and piecewise linear interpolation of nodal values yields suboptimal order estimates. Based on the property of the entire function, we introduce a continuous and piecewise quadratic time reconstruction of the exponential midpoint method to derive optimal order estimates; the error bounds solely depend on the discretization parameters, the data of the problem, and the approximation of the entire function. Several numerical examples are implemented to illustrate the theoretical results.

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.