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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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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Optimizing the Coefficients of Numerical Differentiation Formulae Using Neural Networks
IEEE Access, 2021 The use of a numerical differentiation formula (NDF) is an excellent method for solving stiff ordinary differential equations. However, the NDF method cannot fully adapt to all stiff systems.
Xinyu Yang +3 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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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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Projective Integration for Hyperbolic Shallow Water Moment Equations
Axioms, 2022 In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more
Amrita Amrita, Julian Koellermeier
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Solutions of Stiff Systems of Ordinary Differential Equations Using Residual Power Series Method
Journal of Mathematics, 2022 The stiff differential equations occur in almost every field of science. These systems encounter in mathematical biology, chemical reactions and diffusion process, electrical circuits, meteorology, mechanics, and vibrations. Analyzing and predicting such
Mubashir Qayyum, Qursam Fatima
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New Stable, Explicit, Shifted-Hopscotch Algorithms for the Heat Equation
Mathematical and Computational Applications, 2021 Our goal was to find more effective numerical algorithms to solve the heat or diffusion equation. We created new five-stage algorithms by shifting the time of the odd cells in the well-known odd-even hopscotch algorithm by a half time step and applied ...
Ádám Nagy +4 more
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New S-ROCK methods for stochastic differential equations with commutative noise [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 The class of strong stochastic Runge–Kutta (SRK) methods for stochas tic differential equations with a commutative noise proposed by R¨ oßler (2010) is considered.
A. Haghighi
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An approximate numerical solution of some of the stiff linear boundary values problems of the second order using the method of matching with multiple shooting and interpolation. [PDF]
مجلة التربية والعلم, 2009 The purpose of this research combining the algorithm of superposition with multiple shooting and interpolation designing for solving Stiff linear boundary value problems in ordinary differential equations.
Mohammed Altai, Suhaib Abdulbaqi
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