Mathematicians finally understand the behavior of an important class of differential equations that describe everything from ...

Abstract: The Poisson equation is an elliptic partial differential equation that frequently emerges when modeling electromagnetic systems. However, like many other partial differential equations, ...

This comprehensive volume presents essential mathematical results devoted to topics of mathematical analysis, differential equations and their various applications. It focuses on differential ...

This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, ...

Abstract: Differential-algebraic equations (DAEs) arise naturally as a result of equation-based object-oriented modeling. In many cases, these models contain unknown parameters that have to be ...

The course gives a thorough basis for understanding stochastic dynamics and models. We will in particular study Brownian motion and martingales, Ito’s stochastic calculus, stochastic integration and ...

This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). To improve the ...

optimized rewriting of classical stiff ODES solvers. specialized versions of stabilized explicit solvers, mainly for large systems resulting from parabolic PDEs. Stabilized explicit solvers (Rock*) ...