Index of an Implicit Time-varying Linear Differential Equation: a Noncommutative Linear Algebraic Approach.∗
نویسندگان
چکیده
An intrinsic definition of the index for implicit linear time-varying differential systems is proposed. This definition relies on linear algebraic techniques over the noncommutative principal ideal ring of non-constant linear differential operators (noncommutative transfer function or state-variable representation). Accordance with the existing definition for constant coefficient linear systems is demonstrated.
منابع مشابه
Asymptotic Expansions for Regularization Methods of Linear Fully Implicit Differential-Algebraic Equations
Abstract. Differential-algebraic equations with a higher index can be approximated by regularization algorithms. One of such possibilities was introduced by März for linear time varying index 2 systems. In the present paper her approach is generalized to linear time varying index 3 systems. The structure of the regularized solutions and their convergence properties are characterized in terms of...
متن کاملAn Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients
Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...
متن کاملCubic spline Numerov type approach for solution of Helmholtz equation
We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...
متن کاملAlgebraic Theory of Time-varying Linear Systems: a Survey
The development of the algebraic theory of time-varying linear systems is described. The class of systems considered consists of differential-algebraic equation in kernel presentation. This class encompasses time-varying state space, descriptor systems as well as Rosenbrock systems, and time-invariant systems in the behavioural approach. One difference between time-varying and time-invariant sy...
متن کاملLinear Daes with Nonsmooth Forcing
State transfer functions are derived for linear time invariant differential-algebraic equations of arbitrary index subject to insufficient smoothness in the forcing functions. As a result, it is demonstrated that the problem of reinitialization after discontinuities is always fully and uniquely determined. Algorithmic implementations and extensions to the linear time varying and nonlinear cases...
متن کامل