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Computability of Ordinary Differential Equations [PDF]
, 2018 In this paper we provide a brief review of several results about the computability of initial-value problems (IVPs) defined with ordinary differential equations (ODEs). We will consider a variety of settings and analyze how the computability of the IVP will be affected.
Graça, Daniel, Zhong, Ning
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 We consider a class of retarded functional differential equations with preassigned moments of impulsive effect and we study the Lipschitz stability of solutions of these equations using the theory of generalized ordinary differential equations and ...
Suzete Afonso, Márcia da Silva
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SOLUSI DARI PERSAMAAN CAUCHY–EULER NONHOMOGEN KASUS LOGARITMIK
E-Jurnal Matematika, 2020 Ordinary differential equation is one form of differential equations that are often found in everyday life. One form of ordinary differential equations which has non–constant coefficients is the Cauchy–Euler differential equation.
I GEDE PUTU MIKI SUKADANA +2 more
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Pursuit Curves and Ordinary Differential Equations
Communications, 2012 This paper deals with the differential equations which describe curves of pursuit, in which the pursuer's velocity vector always points directly towards the pursued. We use the Laplace Transform method to solve the classic problem of four mice pursuit.
Zuzana Malacka
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Fault Diagnosis via Neural Ordinary Differential Equations
Applied Sciences, 2021 Implementation of model-based fault diagnosis systems can be a difficult task due to the complex dynamics of most systems, an appealing alternative to avoiding modeling is to use machine learning-based techniques for which the implementation is more ...
Luis Enciso-Salas +2 more
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Neural Ordinary Differential Equations
CoRR, 2018 We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver.
Tian Qi Chen +3 more
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Predicting Ordinary Differential Equations with Transformers
CoRR, 2023 We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in extensive empirical evaluations that our model performs better or on par with existing methods in terms of accurate ...
Becker, S. +4 more
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Characteristic Neural Ordinary Differential Equations
CoRR, 2021 We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an ODE, C-NODE models the evolution of the latent variables as the solution of a family of first-order quasi-linear ...
Xingzi Xu +4 more
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Alexandria Engineering Journal, 2023 In this study, random ordinary differential equations obtained by randomly choosing the coefficients or initial conditions of the ordinary differential equations will be analyzed by the Residual Power Series Method. The initial conditions or coefficients
Mehmet Merdan, Nihal Atasoy
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Backward difference replacements of the space derivative in first order hyperbolic equations [PDF]
, 1983 Two families of two-time level difference schemes are developed for the numerical solution of first order hyperbolic partial differential equations with one space variable.
Khaliq, AQM, Twizell, EH
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