Singularities of algebraic differential equations [PDF]
Advances in Applied Mathematics, 2021 There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of ordinary or partial differential equations.
Markus Lange‐Hegermann +3 more
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Algebraic structure of space and field [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2001 We investigate an algebraic structure of the space of solutions of autonomous nonlinear differential equations of certain type. It is shown that for these equations infinitely many binary algebraic laws of addition of solutions exist.
Z. Z. Khukhunashvili +1 more
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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
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A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control [PDF]
Mathematics, 2020 Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials.
Yongpeng Tai +4 more
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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
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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
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Novel closed-form travelling wave solutions for space-time fractional coupled Boussinesq–Burger model using extended direct algebraic method [PDF]
Scientific ReportsThe nonlinear fractional partial differential equation known as the space-time fractional coupled Boussinesq-Burger equation (S TFcBBE) is examined in this work.
Taha Radwan +4 more
doaj +2 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
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Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States [PDF]
IEEE Transactions on Control of Network Systems, 2022 Phasor measurement units (PMUs) have become instrumental in modern power systems for enabling real time, wide-area monitoring and control. Accordingly, many studies have investigated efficient and robust dynamic state estimation (DSE) methods in order to
Sebastian A. Nugroho +3 more
semanticscholar +1 more source
Differential Algebraic Equations [PDF]
, 2021 AbstractLet H be a Hilbert space and $$\nu \in \mathbb {R}$$ ν ∈ ℝ . We saw in the previous chapter how initial value problems can be formulated within the framework of evolutionary equations.
Christian Seifert +2 more
openaire +2 more sources