Mathematicians have devised a new way to solve higher-order polynomial equations, ushering in a 'dramatic revision of a basic ...

Employing a system of six differential equations derived from Euler's equations for a rotating rigid body, their model creates a plot that shows the best conditions for a strike. "The simulation ...

This project explores and implements a wide range of classical and advanced techniques in the field of numerical analysis and differential equations, combining symbolic ... and interpretation of each ...

The method we are going to use to solve our differential equation and thus the ... that the net flow into each cell is 0 is by writing a linear equation for each cell. The variables in these equations ...

The maximum principle induces an order structure for partial differential equations, and has become an important tool ... The upper and lower solution method, especially its weak version, is presented ...

The US Department of Commerce improperly used the Cohen’s d test to compute the dumping margin in a targeted dumping case, ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Partial differential equations form an essential part of the core mathematics syllabus for undergraduate scientists and engineers. The origins and applications of such equations occur in a variety of ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

What began with a focus on weather forecasting has evolved toward addressing errors in scientific modeling. In the collaborative environment of the Penn State Institute for Computational and Data ...