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Linearised higher variational equations [PDF]
Discrete and Continuous Dynamical Systems, 2013 This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations $\mathrm{LVE}_{\psi}^k$ of a generic autonomous system along a particular solution $\psi$. The main result of this paper is a compact
S. Simon
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Numerical integration of variational equations. [PDF]
Physical Review E, 2010 We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized ...
C. Skokos, E. Gerlach
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Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations
Journal of Low Frequency Noise, Vibration and Active Control, 2019 In this work, the variational iteration algorithm-I with an auxiliary parameter is used for the analytical treatment of the wave equations and wave-like vibration equations.
Hijaz Ahmad, Tufail A. Khan
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Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control [PDF]
SIAM Journal on Scientific Computing, 2021 We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence of neural ...
M. Ainsworth, Justin Dong
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Nonpotentiality of a diffusion system and the construction of a semi-bounded functional [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 The wide prevalence and the systematic variational principles are used in mathematics and applications due to a series of remarkable consequences among which the possibility to establish the existence of the solutions of the initial equations ...
V.M. Savchin, L.T. Huyen
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Differential inequality and non-oscillation of fourth order differential equation [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 The oscillatory theory of fourth order differential equations has not yet been developed well enough. Theresults are known only for the case when the coefficients of differential equations are power functions.
A.A. Kalybay, A.O. Baiarystanov
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Speeded search of the periodic processes of dynamical systems
Trudy Odesskogo Politehničeskogo Universiteta, 2016 Modelling of periodic processes of electromagnetic devices is a complex problem. The task of finding of periodic solutions of nonlinear differential equations is more complex than the Cauchy task of integrating of these equations because it imposes ...
Олександр Леонідович Шпак
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Desimal, 2021 The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations ...
Atika Faradilla +3 more
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Numerical integration of high-order variational equations of ODEs
Applied Mathematics and Computation, 2023 This paper discusses the numerical integration of high-order variational equations of ODEs. It is proved that, given a numerical method (say, any Runge-Kutta or Taylor method), to use automatic differentiation on this method (that is, using jet transport ...
Joan Gimeno +4 more
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Solutions of (2+1)-D & (3+1)-D Burgers Equations by New Laplace Variational Iteration Technique
Axioms, 2023 The new Laplace variational iterative method is used in this research for solving the (2+1)-D and (3+1)-D Burgers equations. This technique relies on the modified variational iteration method and the Laplace transform.
Gurpreet Singh +4 more
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