A Linear Relation Approach to Port-Hamiltonian Differential-Algebraic Equations

Tannakian Approach to Linear Differential Algebraic Groups

Tannaka’s theorem states that a linear algebraic group G is determined by the category of finite-dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.

Differential-Algebraic Approach to Linear Programming

This paper presents a differential-algebraic approach for solving linear programming problems. The paper shows that the differential-algebraic approach is guaranteed to generate optimal solutions to linear programming problems with a superexponential convergence rate. The paper also shows that the path-following interior-point methods for solving linear programming problems can be viewed as a s...

An Unified Approach to Linear Differential Algebraic Equations and Their Adjoint Equations

Linear Differential Algebraic Equations with Constant Coefficients

Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are...

A new approach for solving the first-order linear matrix differential equations

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...