Results 11 to 20 of about 2,601,937 (224)
Numerical methods for ordinary differential equations with applications to partial differential equations [PDF]
, 1983 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The thesis develops a number of algorithms for the numerical solution of ordinary differential equations with applications to partial differential equations.
Khaliq, Abdul Qayyum Masud
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Explicit and implicit methods for second order ordinary differential equations [PDF]
, 1980 A family of explicit formulas is developed for solving a system of second order linear ordinary differential equations with constant coefficients and with initial conditions specified.
Twizell, E H
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Ordinary Differential Equations [PDF]
, 2021 AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem.
Christian Seifert +2 more
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An introduction to regular splines and their application for initial value problems of ordinary differential equations [PDF]
, 1975 This report describes an application of the general method of integrating initial value problems by means of regular splines for equations with movable singularities.
Werner, H
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Kernel Ordinary Differential Equations [PDF]
Journal of the American Statistical Association, 2021 Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow ...
Dai, Xiaowu, Li, Lexin
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Extrapolation methods for first order ordinary differential equations [PDF]
, 1980 Given a system of fist order differential equations, whose coefficient matrix has constant elements, with initial conditions specified, a family of extrapolating algorithms based on Pade approximants to the exponential function is developped.
Twizell, E H
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A Universal Ordinary Differential Equation
Logical Methods in Computer Science, 2020 An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive continuous function $\epsilon(t)$, it has a $\mathcal{C}^\infty$ solution with $| y(t) - \varphi(t) | & ...
Bournez, Olivier, Pouly, Amaury
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A family of difference schemes for fourth order parabolic partial differential equations [PDF]
, 1983 A family of methods is developed for the numerical solution of fourth order parabolic partial differential equations in one- and two-space variables.
Khaliq, AQM, Twizell, EH
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Stiff neural ordinary differential equations [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021 Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems.
Suyong Kim +4 more
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Optical neural ordinary differential equations
Optics Letters, 2023 Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successive cascading of network hidden layers results in larger integrated photonic chip areas. To address this issue, we propose the optical neural ordinary differential equations (ON-ODEs) architecture that parameterizes ...
Yun Zhao +7 more
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