Study of Linear Differential-Algebraic Equations of Higher-Order and Characteristics of Matrix Polynomials

Abstract

This proposition adds to the hypothetical investigation of linear Differential Algebraic Equations of higher order just as of the regularity and singularity of matrix polynomials. Begin with ODE system: y' (=dy/dt) = f(y, t), y(0) = y0

Here we anticipate a development of y in time and there are various methods that guarantee a precise and stable advancement. A few invariant and dense structure under fitting proportionate transformation are given for systems of linear higher order Differential
Algebraic EquationsS with constants and variable coefficients.Inductively, in view of dense structure the first Differential Algebraic EquationsS system can changed by differentiation and elimination ventures into an equql oddness free system , From which the arrangement conduct (counting consistency of starting conditions and remarkable resolvability)of the first Differential Algebraic EquationsS system and related beginning quality problem can be legitimately perused off.It is demonstrated that the accompanying identicalness hold foe a Differential Algebraic Equations system oddness record ^and square and constant coefficient.

For any reliable starting condition any right side ƒ(