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 ...

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

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 ...

In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation ...

K. S. Miller and B. Ross , An Introduction to the Fractional Calculus and Fractional Differential Equations ( John Wiley and Sons , New York , 1993 ) . Google Scholar M. Weilbeer , Efficient Numerical ...

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 way we approach education, particularly in mathematics, has changed a lot over the past few years. As students face increasingly complex math problems, AI-powered tools have emerged as invaluable ...