Results 1 to 10 of about 12,115 (164)
Implicit Fractional Differential Equations via the Liouville–Caputo Derivative
Mathematics, 2015 We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.
Juan J. Nieto +2 more
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Two-parameter families of implicit differential equations
Discrete and Continuous Dynamical Systems, 2005 The author studies first-order implicit ordinary differential equations \(F(x,y,y')=0\) in the neighbourhood of singular points \(q\) with \(F(q)=F_{y'}(q)=0\) and \(F_{y'y'}(q)\neq0\). All singularities of codimension \(2\) are classified by local topological models and their bifurcations in generic two-parameter families of equations are analysed. As
F Tari
exaly +4 more sources
Numerical solutions for implicit differential equations with singularities
Semina: Ciências Exatas e Tecnológicas, 2022 In this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation.
Antonio Castelo +2 more
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An implicit system of delay differential algebraic equations from hydrodynamics
Electronic Journal of Qualitative Theory of Differential Equations, 2023 Direct spring operated pressure relief valves connected to a constantly charged vessel and a downstream pipe have a complex dynamics. The vessel-valve subsystem is described with an autonomous system of ordinary differential equations, while the presence
Fanni Kádár, Gábor Stépán
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Mittag-Leffler Euler ∇-differences for Caputo fractional-order systems
Results in Physics, 2022 Exponential Euler differences have got rapid development recently for integer-order differential equations. But there are few papers focusing on this difference to fractional differential equations.
Tianwei Zhang, Yongkun Li, Jianwen Zhou
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Index of an implicit differential equation [PDF]
Publicacions Matemàtiques, 2010 In the first part of the article, the authors introduce the notion of an index of an implicit ordinary differential equation at an isolated singularity and show that equivalent germs of implicit differential equations possess identical indices. They provide explicit expressions for the case of binary differential equations of degree \(3\).
Challapa, L. S., Ruas, M. A. S.
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Implicit Partial Differential Equations [PDF]
, 1999 Progress in Nonlinear Differential Equations and their Applications ...
B. DACOROGNA, MARCELLINI, PAOLO
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Desingularization of implicit analytic differential equations [PDF]
Journal of Physics A: Mathematical and General, 2006 The question of finding solutions to given implicit differential equations (IDE) has been answered by several authors in the last few years, using different approaches, in an algebraic and also a geometric setting. Many of those results assume in one way or another that the subimmersion theorem can be applied at several stages of the reduction ...
Cendra, Hernan +2 more
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A universal method of solving differential equations in spreadsheet software
Nihon Kikai Gakkai ronbunshu, 2022 We propose a method for solving differential equations implicitly using iterative calculations in spreadsheet software. This method uses difference equations by discretizing the coordinates of the independent variables with cells of spreadsheet for ...
Kiyomi YAMANE +4 more
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On the solvability of initial-value problems for nonlinear implicit difference equations
Advances in Difference Equations, 2004 Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations.
Ha Thi Ngoc Yen, Pham Ky Anh
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