This paper presents some globally convergent descent methods for solving systems of nonlinear equations defined by locally Lipschitzian functions. These methods resemble the well-known family of ...

VideoMath is one of the hardest subjects in school, which is why owning a graphing calculator seems like a necessity for students. But what if you could use your smartphone to solve equations by ...

A new method, combining complex analysis with numerics, is introduced for solving a large class of linear partial differential equations (PDEs). This includes any linear constant coefficient PDE, as ...

The method of moving planes in integral forms These ideas and techniques are illustrated first by simple examples, with the aid of graphs, as necessary. Then, through careful analysis of a series of ...

This example solves a nonlinear system of equations by Newton's method. Let the nonlinear system be represented by F(x) = 0 ...

Additionally, by combining Porous-DeepONet with DeepM&Mnet to address the challenge of solving multiphysics coupled PNP equations, computation times were dramatically reduced by a factor of 50.

In a boon to algebra students everywhere, a professor at Carnegie Mellon University has devised a simpler and more efficient way to solve problems involving the quadratic equation.

A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...