Results 1 to 10 of about 1,287,111 (291)
Algebraic entropy for differential-delay equations [PDF]
arXiv, 2014 We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
Viallet, Claude M.
arxiv +7 more sources
Differential Equations for Algebraic Functions [PDF]
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007 It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions.
Bostan, Alin +4 more
core +13 more sources
Linearisation of a second-order nonlinear ordinary differential equation [PDF]
Acta Polytechnica, 2023 We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v.
Adhir Maharaj +3 more
doaj +3 more sources
Simple algorithm for judging equivalence of differential-algebraic equation systems [PDF]
Scientific Reports, 2023 Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing the difference between equation groups containing multiple equations.
Shota Kato, Chunpu Zhang, Manabu Kano
doaj +2 more sources
On algebraic integrals of a differential equation
Discrete and Continuous Models and Applied Computational Science, 2019 We consider the problem of integrating a given differential equation in algebraic functions, which arose together with the integral calculus, but still is not completely resolved in finite form.
Mikhail D Malykh +2 more
doaj +4 more sources
Converting DAE Models to ODE Models: Application to Reactive Rayleigh Distillation [PDF]
Chemical Engineering Transactions, 2013 This paper illustrates the application of an index reduction method to some differential algebraic equations (DAE) modelling the reactive Rayleigh distillation.
K. Alloula +3 more
doaj +5 more sources
Solutions of algebraic differential equations
Journal of Differential Equations, 1983 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.
Lee A. Rubel
openalex +3 more sources
Algebraic and differential operator equations
Linear Algebra and its Applications, 1988 AbstractExplicit expressions for solutions of boundary-value problems and Cauchy problems related to the operator differential equation X(n)+An−1Xn−1)+⋯+A0X=0 are given in terms of solutions of the algebraic operator equation Xn+An−1Xn−1 +⋯+A0=0. A method for solving this algebraic equation is studied.
L. Jódar
openalex +3 more sources
Dynamic State Estimation of Nonlinear Differential Algebraic Equation Models of Power Networks [PDF]
IEEE Transactions on Power Systems, 2022 This paper investigates the joint problems of dynamic state estimation of algebraic variables (voltage and phase angle) and generator states (rotor angle and frequency) of nonlinear differential algebraic equation (NDAE) power network models, under ...
Muhammad Nadeem +2 more
semanticscholar +1 more source
Index concepts for differential-algebraic equations
, 2012 We discuss several of different index concepts for differential-algebraic equation (differentiation, strangeness, tractability, geometric, perturbation, and structural index) and analyze their relationship.
V. Mehrmann
semanticscholar +3 more sources