International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2018, Vol. 3, Issue 2, Part F

Theoretical concept of linear higher and algebraic equations


Author(s): Roji Lather

Abstract: This paper contributes to the theoretical analysis of linear Differential Algebraic Equations of higher order as well as of the regularity and singularity of ma­trix polynomials. An algebraic number field is a finite extension field of the field of rational numbers. Within an algebraic number field is a ring of algebraic integers, which plays a role similar to the usual integers in the rational numbers.Some invariants and condensed forms under appropriate equivalent transformations are given for systems of linear higher-order Differential-Algebraic Equations’ with constant and variable coefficients. Inductively, based on condensed forms the original Differential-Algebraic Equations system can be transformed by differentiation-and-elimination steps into an equivalent strangeness-free system, from which the solution behaviour (including consistency of initial conditions and unique solvability) of the original Differential-Algebraic Equations system and related initial value problem can be directly read off. It is shown that the following equivalence holds for a Differential-Algebraic Equations system with strangeness-index ^ and square and constant coefficients. For any consistent initial condition and any right-hand side 3-2-56 the associated initial value problem has a unique solution if and only if the matrix polynomial associated with the system is regular.

Pages: 434-442 | Views: 386 | Downloads: 7

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How to cite this article:
Roji Lather. Theoretical concept of linear higher and algebraic equations. Int J Stat Appl Math 2018;3(2):434-442.
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