Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

Accurately modeling steady-state two-phase flow is critical for the design and operation of systems in the oil and gas industry; however, traditional models often struggle to adapt to specific field ...

Python hunter Kevin Pavlidis won for the third time in 2025. The competition is sponsored by the South Florida Water ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

Leevan Ling and Manfred R Trummer. Adaptive multiquadric collocation for boundary layer problems. Journal of Computational and Applied Mathematics, 188(2):265–282, 2006. Richard Baltensperger and ...

Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful method for solving differential equations by leveraging machine learning techniques. However, while neural ...

The parabolic equation (PE) serves as a fundamental methodology for modeling underwater acoustic propagation. The computational efficiency of this approach derives from the far-field approximation of ...

To derive Newton's method, it is convenient to start with a Taylor series expansion of the residual function: $$ R(u_i) = R(u_{i-1}) + \frac{\partial \textbf{R ...

A modular framework implementing Physics-Informed Neural Networks (PINNs) with Gradient Normalization for solving differential equations including Navier-Stokes equations for crystal growth modeling.