Numerical Methods and Analysis for Partial Differential Equations

Dear Colleagues,

We would like to invite you to submit your original research or review articles to this Special Issue of Mathematics, "Numerical Methods and Analysis for Partial Differential Equations". It focuses on advancing numerical methods used for in-depth studies of the behavior of partial differential equations, including those that increase accuracy and those that behave similarly to the theoretical solutions of partial differential equations. We place emphasis on both the introduction of new numerical methods and the theoretical study of their behavior and approximation errors.

This Special Issue aims to cover the study of models in physics and chemistry, such as the tissue growth model, those that model Klein–Gordon equations, Maxwell–Lorentz equations, Schrödinger equations, Gross–Pietaski equations, heat equations, Dirac equations, Bose–Einstein condensate equations, etc., population models, and models used in the field of economics. It seeks to address the increasing complexity of effective numerical methods that are used for approximating the results and behavior of equations, such as those hitherto mentioned, in various areas, including mass shell conservation, energy conservation, structure preservation, high-oscillatory solutions in space and time, etc.

Typically, mathematical research in this field either pertains to the construction of new methods and improving features within existing methods or the creation or combination of new methods to improve the agreement between modeling results and those obtained theoretically.

Numerical methods can also be used to discern the properties of equations from a continuum perspective, both in terms of existence and uniqueness or continuity with respect to initial conditions.

Furthermore, given the rise in studies of economic models and samplers for Hamiltonian problems, we also seek papers that explore numerical methods applied to stochastic partial differential equations. Numerical methods that demonstrate the behavior of solutions to these equations are of particular interest.

We welcome contributions that exemplify the interdisciplinary potential of mathematics to improve the most widely used models in physics, chemistry, economics, population studies, and so on.

Prof. Dr. Cesáreo González
Guest Editor

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.

• exponential numerical methods
• pseudospectral methods
• finite element methods
• finite difference methods
• physical and chemistry models
• economic models
• qualitative properties of the models
• numerical methods for evolution equations
• qualitative properties of the numerical methods