In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

This paper presents a numerical meshless approach for solving the two-dimensional Allen-Cahn equation, utilizing a radial basis function-compact finite difference (RBF-CFD) method in combination with ...

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can ...

Learn methods for interpolation, numerical integration and derivation, and finite difference methods for differential equations. You can use these live scripts as demonstrations in lectures, class ...

Beam is one of the common structures in engineering, with the development of technology, homogeneous beams no longer meet the needs of engineering structural design, for this reason, people have ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

What Are FEM, FDM and FVM? FEM, FDM and FVM differ from one another in important ways. Understanding these distinctions is key to selecting the method most appropriate for your purposes. The ...

Numerical simulation of three-dimensional (3D) seismic wavefields forms the basis of the research on the migration methods of 3D seismic data based on wave equations. Because the simulation precision ...

Abstract: Partial differential equations (PDEs) are ubiquitous in physics and engineering and used for understanding various physical phenomena, including heat, diffusion, fluid and electrodynamics, ...

Mean field games (MFG) and mean field control (MFC) play central roles in a variety of scientific disciplines such as physics, economics, and data science. While the mathematical theory of MFGs has ...