Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Numerical Approaches for Solving Nonlinear Equations and Systems
share announcement

Numerical Approaches for Solving Nonlinear Equations and Systems

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 980

Special Issue Editors

Prof. Dr. Asai Asaithambi

E-Mail Website
Guest Editor
School of Computing, University of North Florida, Jacksonville, FL 32224, USA
Interests: numerical methods; scientific computing; pattern recognition; robot coalition; energy-aware cybersecurity; machine learning
Prof. Dr. Nan Jiang

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Interests: numerical analysis; entropy convergence analysis; nonlinear hyperbolic conservation laws

Special Issue Information

Dear Colleagues,

Understanding real-life phenomena observed in the life, physical, and social sciences and engineering has been aided by mathematical and computational modelling. Nonlinear equations and systems arise in the modelling of a wide variety of problems of astrophysics, chemical reactions, economics, electronic circuits, fluid flow, gene propagation, heat transfer, kinematics, population growth, and so on. While these applications appear to be varied in the problems they model, and although they might lead to different classes of nonlinear equations and systems, they share a common mathematical theme of initial- and boundary-value problems in ordinary and partial differential equations. The major difficulties encountered in the mathematical theory of nonlinear systems are attributed to factors such as the nature of the nonlinearity and the geometry involved. For this reason, the development of robust and accurate numerical methods for use in nonlinear equations and systems continues to be a great challenge, and this Special Issue will be focused on numerical approaches to solving such systems.

Prof. Dr. Asai Asaithambi
Prof. Dr. Nan Jiang
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear equations and systems
  • ordinary and partial differential equations
  • initial and boundary value problems
  • numerical methods
  • finite differences and finite elements
  • coordinate transformations
  • pseudospectral methods

Published Papers (1 paper)

Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

19 pages, 340 KiB  
Article
On the Convergence of α Schemes with Source Terms for Scalar Convex Conservation Laws
by Nan Jiang
Mathematics 2023, 11(15), 3267; https://doi.org/10.3390/math11153267 - 25 Jul 2023
Viewed by 577
Abstract
In this study, we use an extension of Yang’s convergence criterion [N. Jiang, On the wavewise entropy inequality for high-resolution schemes with source terms II: the fully discrete case] to show the entropy convergence of a class of fully discrete α schemes, [...] Read more.
In this study, we use an extension of Yang’s convergence criterion [N. Jiang, On the wavewise entropy inequality for high-resolution schemes with source terms II: the fully discrete case] to show the entropy convergence of a class of fully discrete α schemes, now with source terms, for non-homogeneous scalar convex conservation laws in the one-dimensional case. The homogeneous counterparts (HCPs) of these schemes were constructed by S. Osher and S. Chakravarthy in the mid-1980s [A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws (1985), Very High Order Accurate TVD Schemes (1986)], and the entropy convergence of these methods, when m=2, was settled by the author [N. Jiang, The Convergence of α Schemes for Conservation Laws II: Fully-Discrete]. For semi-discrete α schemes, with or without source terms, the entropy convergence of these schemes was previously established (for m=2) by the author [N. Jiang, The Convergence of α Schemes for Conservation Laws I: Semi-Discrete Case]. Full article
(This article belongs to the Special Issue Numerical Approaches for Solving Nonlinear Equations and Systems)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-1
Back to TopTop