A reliable direct numerical treatment of differential–algebraic equations by overdetermined collocation : An operator approach

• Recently reported experiments and theoretical contributions concerning overdetermined polynomial collocation applied to higher-index differential–algebraic equations give rise to the conjecture that next to the existing derivative-array based methods there is further potential toward a reliable direct numerical treatment of DAEs. By analyzing first-order differential–algebraic operators and their special approximations in detail, we contribute to justify the overdetermined polynomial collocation applied to first-order higher-index differential–algebraic equations and fill the hitherto existing gap between the theoretical convergence results and its practical realization. Moreover, we shortly touch related questions for higher-order DAEs. We discuss several practical aspects of higher-order differential–algebraic operators and the associated equations which may be important for the application of collocation methods.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Differential–algebraic operator

Essentially ill-posed problem

Higher index

Higher-order differential–algebraic equation

Least-squares problem

Overdetermined polynomial collocation

Differential equations

Polynomials

Algebraic equations

Ill posed problem

Least squares problems

Polynomial collocation

Numerical methods

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)