Scientific American

Master of chaos wins $3-million math prize for ‘blowing up’ equations

It’s the same math that explains how, under the right conditions, the atmosphere above a barren plain can produce a roiling ...
American Institute of Physics

Modeling ice clouds as nonlinear oscillators

Applying a few simplifying assumptions and constructing a set of ordinary differential equations leads to a model that ...
marktechpost

A Coding Guide to Implement Advanced Differential Equation Solvers, Stochastic Simulations, and Neural Ordinary Differential Equations Using Diffrax and JAX

In this tutorial, we explore how to solve differential equations and build neural differential equation models using the Diffrax library. We begin by setting up a clean computational environment and ...
acm.org

On the numerical solution of boundary value problems for linear ordinary differential equations

A numerical method is presented for the solution of boundary value problems involving linear ordinary differential equations. The method described is noniterative and makes use of any one-step ...
IEEE

Error Oriented Tau Method for Systems of Linear Ordinary Differential Equations with Polynomial Coefficients

Abstract: An effective approach to produce an approximate analytical solution to a system of linear ordinary differential equation with polynomial coefficients, is considered. This approach is a ...
IEEE

Unified Framework for Evaluating Numerical Integration Methods Through Characteristic Root Distortion in Linear Ordinary Differential Equations

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

On the numerical solution of an N-point boundary value problem for linear ordinary differential equations

A method for the numerical solution of the n-point boundary value problem for homogeneous linear ordinary differential equations is developed. The method requires two Runge-Kutta integrations over the ...
Frontiers

Applying neural ordinary differential equations for analysis of hormone dynamics in Trier Social Stress Tests

Introduction: This study explores using Neural Ordinary Differential Equations (NODEs) to analyze hormone dynamics in the hypothalamicpituitary-adrenal (HPA) axis during Trier Social Stress Tests ...