Questions concerning differential-algebraic operators: Toward a reliable direct numerical treatment of differential-algebraic equations
Provides theoretical justification for numerical methods used in solving higher-index differential-algebraic equations, which is a niche area in numerical analysis.
The paper investigates differential-algebraic operators to justify overdetermined polynomial collocation for higher-index differential-algebraic equations, addressing practical aspects of higher-order operators.
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and contribute to justify the overdetermined polynomial collocation applied to higher-index differential-algebraic equations. Besides, we discuss several practical aspects concerning higher-order differential-algebraic operators and the associated equations.