Publications related to Differential-algebraic system of equations

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Junming Duan

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Julien Gilles Edgar Gateau

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after e ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2020

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

Machine learning for fast and reliable solution of time-dependent differential equations

Alfio Quarteroni, Francesco Regazzoni

We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential Equations (ODEs) or time-dependent Partial Differential Equations (PDEs). Unlike ...

2019

Solving differential equations with topological acoustic metamaterials

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

The conventional idea of analog computing has recently been revived by recent developments of the fields of metamaterials and ultrafast optics, allowing one to perform signal-processing tasks at the speed of wave propagation with high efficiency. Despite t ...

2019

Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks

Jean-Yves Le Boudec, Mario Paolone, Andrey Bernstein, Cong Wang

We present explicit sufficient conditions that guarantee the existence and uniqueness of the load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the problem, we also account ...

2018

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

Alfio Quarteroni, Michel Deville, Simone Deparis, Luca Pegolotti, Filippo Menghini

We consider the Rosenbrock methods, namely a family of methods for Differential Algebraic Equations, for the solution of the unsteady three-dimensional Navier-Stokes equations. These multistage schemes are attractive for non-linear problems because they ac ...

2018

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Differential-algebraic system of equations

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Confronting false discoveries in single-cell differential expression

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Machine learning for fast and reliable solution of time-dependent differential equations

Solving differential equations with topological acoustic metamaterials

Modeling spatially dependent functional data via regression with differential regularization

Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

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Chat with Graph Search

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Solving differential equations with topological acoustic metamaterials

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Machine learning for fast and reliable solution of time-dependent differential equations

Confronting false discoveries in single-cell differential expression

Modeling spatially dependent functional data via regression with differential regularization

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks