Related papers: Index definitions for nonlinear IAEs and DAEs: new…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…
In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of differential algebraic equations (DAEs). A multivariate…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and…
We study integrated semigroups for infinite-dimensional differential-algebraic equations (DAEs) admitting a resolvent index. Building on the notion of integrated semigroups for the abstract Cauchy problem $\frac{d}{d t}x=Ax$, we extend this…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of…
We study a deflation method to reduce and to solve linear dfferential-algebraic equations (DAEs). It consists to define a sequence of DAEs with index reduction of one unit by step. This is simultaneously performed by substitution and…
We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also…
We consider a class of differential-algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the…
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper…
This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challenging in machine learning. Integral equations (IEs), which…
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…