Results 11 to 20 of about 7,875,654 (350)
Variations for Some Painlevé Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 This paper first discusses irreducibility of a Painlevé equation $P$. We explain how the Painlevé property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we associate an autonomous Hamiltonian $\mathbb{H}$ to a Painlevé equation $P$.
Acosta-Humañez, Primitivo B. +2 more
openaire +4 more sources
Stability of Difference Equations and Applications to Robustness Problems
Advances in Difference Equations, 2010 The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems.
Bogdan Sasu
doaj +2 more sources
A variational approach to the shock structure problem [PDF]
Theoretical and Applied Mechanics, 2005 A variational approach to the shock structure problem is proposed. The set of governing equations, consisted of n first-order ordinary differential equations accompanied with 2n boundary conditions at ±∞, is put into variational form by means of least ...
Simić Srboljub S.
doaj +1 more source
Second-order variational equations for N-body simulations [PDF]
, 2016 First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for e cient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic ...
H. Rein, D. Tamayo
semanticscholar +1 more source
An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs [PDF]
Applied Mathematics and Computation, 2015 An algorithm for validated computation of monodromy matrices for ODEs is provided.Smaller truncation error allows larger time steps making the computation faster.The existence of a chaotic and hyperbolic set for the Rossler system is proved via computer ...
Irmina Walawska, D. Wilczak
semanticscholar +1 more source
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order ...
E. Kharazmi +2 more
semanticscholar +1 more source
Variational Physics-informed Neural Operator (VINO) for solving partial differential equations [PDF]
Computer Methods in Applied Mechanics and EngineeringSolving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or boundary ...
M. Eshaghi +5 more
semanticscholar +1 more source
, 2004 Variational integrators are a class of discretizations for mechanical systems which are derived by discretizing Hamilton's principle of stationary action.
West, Matthew
core +1 more source
Different Groups of Variational Principles for Whitham-Broer-Kaup Equations in Shallow Water [PDF]
Journal of Applied and Computational Mechanics, 2020 Because the variational theory is the theoretical basis for many kinds of analytical or numerical methods, it is an essential but difficult task to seek explicit functional formulations whose extrema are sought by the nonlinear and complex models. By the
Xiao-Qun Cao +4 more
doaj +1 more source
Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
core +2 more sources