Results 21 to 30 of about 80,042 (308)
On numerical integration of implicit ordinary differential equations [PDF]
, 1981 summary:In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential
Kwapisz, Marian, Jackiewicz, Zdzisław
core +1 more source
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
openaire +5 more sources
Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations [PDF]
, 2011 By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure ...
Wu, Fuke +5 more
core +1 more source
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
doaj +1 more source
Asymptotic behaviours of stochastic differential delay equations [PDF]
, 2005 Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi +3 more
core +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
Asymptotic solvers for ordinary differential equations with multiple frequencies [PDF]
, 2015 We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies.
Iserles, Arieh +3 more
core +2 more sources
Solving Ordinary Differential Equations with Discontinuities [PDF]
ACM Transactions on Mathematical Software, 1984 Automatic codes for differential equations can be inadequate when the solutions have discontinuities. If the user provides an external indicator for discontinuities (e.g., a switching function whose sign changes indicate discontinuities), a code can be more efficient.
Gear, C. W., Østerby, Ole
openaire +4 more sources