Quanta Magazine

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

Simultaneous packing structures in superionic water may explain ice giant magnetic fields

Superionic water—the hot, black and strangely conductive form of ice that exists in the center of distant planets—was ...
Science Daily

These mesmerizing patterns are secretly solving hard problems

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

Neural ODE Model of Power Electronic Converters With Accelerated Computation and High Fidelity

Abstract: Nowadays, conducting detailed numerical simulation of power electronic (PE) converters is time-consuming due to the iterative solution of nonlinear equations. While simplified numerical ...
IEEE

Iterative Sparse Identification of Nonlinear Dynamics

Abstract: In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful ...
Scientific Research Publishing

Wazwaz, A. (2007) The Variational Iteration Method for Exact Solutions of Laplace Equation. Physics Letters A, 363, 260-262.

ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...
Scientific Research Publishing

Ortega, J.M. and Rheinboldt, W.G. (1970) Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York.

ABSTRACT: In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations ...