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

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and ...

The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones. The results obtained by treating the ...

This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The ...

For dissipative partial differential equations the Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips ...

Ordinary Differential Equations. Introduction to methods for finding solutions to differential equations involving a single, independent variable. Topics include linear equations, exact solutions, ...

This chapter contains sections titled: Introduction Differential Equations for a Uniform Line with AC Excitation Transmission-line Equations for a Uniform ...

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.

We will present stochastic dynamical models via stochastic differential equations and study existence and uniqueness of solutions, linear stochastic differential equations, theory for diffusion ...

Course information Learning outcomes After the course student knows - how to solve partial differential equations using separation of variables and Fourier techniques - the physical interpretations of ...

Mathematics is the universal language of science while computer science is the study of the hardware and algorithms that are used in modern computer systems. Since many of the early pioneers of ...

The Department of Mathematics and Statistics was host until 2014 to the MSc course in the Mathematics of Scientific and Industrial Computation (previously known as Numerical Solution of Differential ...