Advances in Numerical Analysis of Partial Differential Equations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 1552

Special Issue Editor


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Guest Editor
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Interests: numerical analysis and partial differential equations

Special Issue Information

Dear Colleagues,

‘Advances in Numerical Analysis of Partial Differential Equations’ provides a suitable platform for the development of original research in the fields of numerical solutions for partial differential equations from science and engineering. The purpose of this Special Issue is to gather contributions from experts on numerical analysis and scientific computing with application domains, including, but not limited to, computational fluid dynamics, hyperbolic conservation laws, shallow water equations, magnetohydrodynamics, relativistic fluid mechanics, and actuators. Contributions should have a main emphasis on numerical methods for the innovation of the method and their applications.

Prof. Dr. Gang Li
Guest Editor

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Keywords

  • high-order accuracy
  • partial differential equations
  • physical-constraint-preserving property
  • science and engineering

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Published Papers (2 papers)

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Research

13 pages, 386 KiB  
Article
Reachable Set Estimation of Discrete Singular Systems with Time-Varying Delays and Bounded Peak Inputs
by Hongli Yang, Lijuan Yang and Ivan Ganchev Ivanov
Mathematics 2025, 13(1), 79; https://doi.org/10.3390/math13010079 - 28 Dec 2024
Cited by 1 | Viewed by 569
Abstract
This paper studies the estimation of reachable sets for discrete-time singular systems with time-varying delays and bounded peak inputs. A novel linear matrix inequality condition for the reachable set estimation of the time-varying time-delay discrete singular system is derived using an inverse convex [...] Read more.
This paper studies the estimation of reachable sets for discrete-time singular systems with time-varying delays and bounded peak inputs. A novel linear matrix inequality condition for the reachable set estimation of the time-varying time-delay discrete singular system is derived using an inverse convex combination and the discrete form of the Wirtinger inequality. Furthermore, the symmetric matrix involved in the obtained results does not need to be positively definite. Compared to decomposing the time-delay discrete singular system under consideration into fast and slow subsystems, the method presented in this paper is simpler and involves fewer variables. Two numerical examples are provided to illustrate the proposed method. Full article
(This article belongs to the Special Issue Advances in Numerical Analysis of Partial Differential Equations)
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19 pages, 1385 KiB  
Article
A Solution-Structure B-Spline-Based Framework for Hybrid Boundary Problems on Implicit Domains
by Ammar Qarariyah, Tianhui Yang and Fang Deng
Mathematics 2024, 12(24), 3973; https://doi.org/10.3390/math12243973 - 18 Dec 2024
Cited by 1 | Viewed by 719
Abstract
Solving partial differential equations (PDEs) on complex domains with hybrid boundary conditions presents significant challenges in numerical analysis. In this paper, we introduce a solution-structure-based framework that transforms non-homogeneous hybrid boundary problems into homogeneous ones, allowing exact conformity to the boundary conditions. By [...] Read more.
Solving partial differential equations (PDEs) on complex domains with hybrid boundary conditions presents significant challenges in numerical analysis. In this paper, we introduce a solution-structure-based framework that transforms non-homogeneous hybrid boundary problems into homogeneous ones, allowing exact conformity to the boundary conditions. By leveraging B-splines within the R-function method structure and adopting the stability principles of the WEB method, we construct a well-conditioned basis for numerical analysis. The framework is validated through a number of numerical examples of Poisson equations with hybrid boundary conditions on different implicit domains in two and three dimensions. The results reflect that the approach can achieve the optimal approximation order in solving hybrid problems. Full article
(This article belongs to the Special Issue Advances in Numerical Analysis of Partial Differential Equations)
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