Numerical Methods for Partial Differential Equation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 809

Special Issue Editor


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Guest Editor
School of Mathematics and Natural Sciences, University of Southern Mississippi, Hattiesburg, MS 39406, USA
Interests: computational neuroscience; high performance computing; deep learning; neural networks; weak Galerkin FEM and VEM; numerical analysis for nonlocal PDEs

Special Issue Information

Dear Colleagues,

Numerical methods for partial differential equations (PDEs) are a set of techniques used to solve PDE models computationally. Many problems in a wide range of sciences require such solutions. This Special Issue aims to collect original and novel contributions in the field of numerical methods for PDEs on polygonal/polyhedral meshes, including the Weak Galerkin method, the Hybrid Discontinuous method, the Virtual Element method, the Hybrid High-Order method, and other related methods. Topics will cover numerical analysis, mesh generation, and applications of these methods.

Dr. Qingguang Guan
Guest Editor

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Keywords

  • polygonal/polyhedral meshes
  • weak Galerkin method
  • hybrid discontinuous method
  • virtual element method
  • hybrid high-order method
  • numerical analysis
  • partial differential equations (PDEs)
  • mesh generation

Published Papers (1 paper)

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Research

9 pages, 440 KiB  
Article
Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation
by Weifang Yan, Linlin Wang and Min Zhang
Mathematics 2024, 12(6), 928; https://doi.org/10.3390/math12060928 - 21 Mar 2024
Viewed by 545
Abstract
In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the bifurcation method of dynamical systems. Then, the [...] Read more.
In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the bifurcation method of dynamical systems. Then, the persistence of the kink and antikink wave solutions of the perturbed modified Gardner equation is studied by exploiting the geometric singular perturbation theory and the Melnikov function method. When the perturbation parameter is sufficiently small, we obtain the sufficient conditions to guarantee the existence of kink and antikink wave solutions. Full article
(This article belongs to the Special Issue Numerical Methods for Partial Differential Equation)
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