Results 11 to 20 of about 7,385 (298)
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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Exponential Multistep Methods for Stiff Delay Differential Equations
Axioms, 2022 Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms.
Rui Zhan +3 more
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Mendel, 2022 This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti +2 more
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Extrapolation at stiff differential equations
Numerische Mathematik, 1988 Asymptotic expansions for the global error for extrapolation methods using the implicit Euler method, the linearly implicit Euler method and the linearly implicit midpoint rule for stiff initial value problems in ordinary differential equations are derived. Practical implications of these results for error estimation and step-size control are indicated.
Hairer, E., Lubich, C.
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Differential/Algebraic Equations As Stiff Ordinary Differential Equations
SIAM Journal on Numerical Analysis, 1992 To a system of differential algebraic equations: \[ \text{(DAE)}\quad y'(t)=f(t,y(t),z(t),0),\quad g(t,y(t),z(t),0)=0, \] a system of singularly perturbed ordinary differential equations: \[ \text{(ODE)}\quad y_ \varepsilon'(t)=f(t,y_ \varepsilon(t),z_ \varepsilon(t),\varepsilon), \varepsilon z_ \varepsilon'(t)=g(t,y_ \varepsilon(t),z_ \varepsilon(t ...
exaly +5 more sources
Explicit Methods for Stiff Stochastic Differential Equations [PDF]
, 2011 Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-square stable) stiff stochastic differential equations. Standard explicit methods, as for example the
Assyr Abdulle, Abdulle, Assyr
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Haar wavelet method for solving stiff differential equations
Mathematical Modelling and Analysis, 2009 Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered.
Ülo Lepik
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A novel hybrid framework for efficient higher order ODE solvers using neural networks and block methods [PDF]
Scientific ReportsIn this paper, the author introduces the Neural-ODE Hybrid Block Method, which serves as a direct solution for solving higher-order ODEs. Many single and multi-step methods employed in numerical approximations lose their stability when applied in the ...
V. Murugesh +7 more
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Error estimators for stiff differential equations
Journal of Computational and Applied Mathematics, 1984 The quality of error estimators is specially important when solving stiff problems by step methods. The authors consider one-step methods for: \(y'=f(y)\), \(y(a)=y_ 0\), \(a\leq x\leq b\), and show how to improve the estimators applying a technique of linearisation used frequently in stability analyses.
Shampine, Lawrence F., Baca, Lorraine S.
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Haar wavelet collocation method for linear first order stiff differential equations [PDF]
ITM Web of Conferences, 2020 In general, there are countless types of problems encountered from different disciplines that can be represented by differential equations. These problems can be solved analytically in simpler cases; however, computational procedures are required for more ...
Atay Mehmet Tarık +4 more
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