Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest ...

This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied ...

The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous ...

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

To locate as many roots as possible of nonlinear equation systems, in this paper, a co-evolutionary dual niching differential evolution with information sharing and migration is developed. To be ...

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.

py-pde is a Python package for solving partial differential equations (PDEs). The package provides classes for grids on which scalar and tensor fields can be defined. The associated differential ...

Abstract: Electrical models of linear partial differential equations may serve several practical purposes: 1. If the networks are physically constructed, they actually may solve the equations within ...

or “How likely is it to find 2 defective items in a box of 5?” This distribution is built on a type of process called a Bernoulli sequence—a series of independent trials with constant probability of ...

The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...