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Exponential Runge-Kutta methods for stiff kinetic equations [PDF]
SIAM Journal on Numerical Analysis, 2010 We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK ...
Dia B. O. +4 more
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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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Some Techniques for Solving “Stiff” Equations [PDF]
Bulletin of the Polytechnic Institute of Jassy: Constructions, Architechture Section, 2005 The Structural Dynamics involves a large amount of computational effort. Most dynamic structural models require the solution of a set of 2nd order differential equations.
Victor-Octavian Roşca
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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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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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