Manuscript Topics

Most of the models appearing in applied sciences and engineering technology, such as biology, physics, network science, medicine can be described by integer- and fractional-order partial differential equations (PDEs). However, the exact solutions of such PDEs are often unavailable, numerical methods (e.g., finite difference method, finite element method, etc.) become the mainstream tools for solving these PDEs. Although numerical methods for integer- and fractional-order PDEs get a booming development in the past several decades, the numerical methods can accurately maintain the important characteristics or structures of these equations such as energy stability or dissipation, optimal long-time decay rate, long-term numerical stability or convergence of numerical schemes for such PDEs are still limited. Therefore, developing the numerical solutions of integer- and fractional-order PDEs is still quite challenging in the field of (computational) mathematics.

The main aim of this Special Issue is to focus on some recent developments in efficient solutions of integer- and fractional-order PDEs including numerical and theoretical results. All the articles and reviews devoted to the above theme on numerical methods of such PDEs and their applications are welcome.

Topics of interest include, but are not limited to:

• Finite element, finite difference, finite volume methods
• Error estimate and stability analysis
• Parallel-in-time method
• Spectral/collocation method

• Multigrid method
• Domain decomposition method
• Model order reduction

• Numerical methods for ordinary/stochastic differential equations
• Machine learning algorithm
• Numerical methods for integral and integro-differential equations

Instructions for authors

https://www.aimspress.com/nhm/news/solo-detail/instructionsforauthors

Please submit your manuscript to online submission system

https://aimspress.jams.pub/