In this paper, we prepare the analysis of differential-algebraic equations (DAEs) with regard to properties as positivity, stability or contractivity. To study these properties, the differential and algebraic components of a DAE must be separated to quantify when they exhibit the desired property. For the differential components, the common results for ordinary differential equations (ODEs) can...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

Using power series methods, Harris and Sibuya [3, 4] recently showed that if A: is an ordinary differential field of characteristic zero and y 5¿ 0 is an element of a differential extension of fc such that y and l/y satisfy linear differential equations with coefficients in fc, then y'¡y is algebraic over fc. Using differential galois theory, we generalize this and characterize those polynomial...

Abstract We investigate genericity of various controllability and stabilizability concepts linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations these (see the survey article by Berger Reis (in: Ilchmann A, T (eds) Surveys in equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1 )), we use too...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing pcurvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P1−{0, 1,∞}. We prove a variant of this conjecture for P1−{0, 1,∞}, which asserts that if the equation satisfies a certain conve...

This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants. We give the simplest example of this, that every C” solution of an ADE satisfi...

—This document presents an introduction of two commonly used power system differential algebraic equations for studying electromechanical oscillation and transient stability. Two types of generator models are used to formulate the power system model, respectively: the second-order classical model and the fourth-order generator model. An example is provided on the IEEE 9-bus system.

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....