MAXIMUM ERROR ESTIMATES OF DISCONTINUOUS GALERKIN METHODS FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Hongyu Qin; Yuanyuan Li; Fengyan Wu

doi:10.11948/20240386

2025 Volume 15 Issue 4

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Hongyu Qin, Yuanyuan Li, Fengyan Wu. MAXIMUM ERROR ESTIMATES OF DISCONTINUOUS GALERKIN METHODS FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2027-2043. doi: 10.11948/20240386

Citation:

Hongyu Qin, Yuanyuan Li, Fengyan Wu. MAXIMUM ERROR ESTIMATES OF DISCONTINUOUS GALERKIN METHODS FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2027-2043. doi: 10.11948/20240386

MAXIMUM ERROR ESTIMATES OF DISCONTINUOUS GALERKIN METHODS FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS

1.
School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China
2.
College of Mathematics and Statistics, and Key Laboratory of Nonlinear Analysis and its Applications (Chongqing University), Ministry of Education, Chongqing University, Chongqing 401331, China

Author Bio: Email: qinhy@wit.edu.cn(H. Qin); Email: yuanyuanli_wit@hotmail.com(Y. Li)
Corresponding author: Email: fywuhust@163.com(F. Wu)

Abstract

Abstract

The exact solution to a neutral delay differential equation is generally non-smooth. Some possible loss of accuracy is usually found if certain high-order numerical methods are applied. The discontinuous Galerkin (DG) methods are introduced to numerically solve neutral delay differential equations so as to handle the difficulties. Maximum error estimates of the numerical method is investigated. Theoretical results indicate that the ${p}$-degree DG approximate solution has an accuracy of ${p}$-th order. Numerical experiments are presented to confirm the effectiveness and performance of the DG methods.
- Neutral delay differential equations /
- maximum error estimates /
- discontinuous Galerkin methods
MSC: 65L60, 65L70

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References

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