A Research Upon Architectural Assessment and Numerical Solution of Differential Algebraic Equations: A Comprehensive Study on the Structural Properties and Numerical Treatment of Differential-Algebraic Equations

Abstract

Systems of Differential-Algebraic Equations (DAEs) havebeen widely investi­gated, during the last twenty years, from a numerical pointof view. In this paper, our interest is in the study of formal("structural") properties of DAE systems: we make the link betweenthe index of a DAE system and general notions coming from the formal theory of PDEs. This interpretation gives new insights for the understanding of DAE s andallows us to give rigorous justification of manipulations that, are of usualpractice in this area. Differential-algebraic equations (DAEs) arise in avariety of applications. Therefore their analysis and numerical treatment playsan important role in modern mathematics. This paper gives an introduction tothe topic of DAEs. Examples of DAEs are considered showing their importance forpractical problems. Several well-known index concepts are introduced. In thecontext of the tractability index existence and uniqueness of solutions for lowindex linear DAEs is proved. Numerical methods applied to these equations arestudied.