Paired explicit Runge-Kutta schemes for stiff systems of equations [PDF]
Journal of Computational Physics, 2019 In this paper we introduce a family of explicit Runge-Kutta methods, referred to as Paired Explicit Runge-Kutta (P-ERK) schemes, that are suitable for the solution of stiff systems of equations.
Brian C. Vermeire
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Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
, 2021 The recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network such that the network not only conforms to the ...
Zhiyu Shi (11361373) +9 more
core +2 more sources
Two-stage single ROW methods with complex coefficients for autonomous systems of ODE [PDF]
Компьютерные исследования и моделирование, 2010 The basic subset of two-stage Rosenbrock schemes with complex coefficients for numerical solution of autonomous systems of ordinary differential equations (ODE) has been considered. Numerical realization of such schemes requires one LU-decomposition, two
Petr Dmitrievich Shirkov +1 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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A Portable Stiffness Measurement System [PDF]
Sensors, 2017 A new stiffness measurement method is proposed that utilizes the lateral deformation profile of an object under indentation. The system consists of a force measurement module between a pair of equidistant touch sensing modules. Unique feature of the method is that by adjusting the touch module separation, indenter protrusion, and spring constant of the
Onejae Sul, Eunsuk Choi, Seung-Beck Lee
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The Numerical Solution of Differential and Differential-Algebraic Systems [PDF]
Modeling, Identification and Control, 1985 Systems of ordinary differential equations (ODE) or ordinary differential/algebraic equations (DAE) are well-known mathematical models. The numerical solution of such systems are discussed. For (ODE) we mention some available codes and stress the need of
Syvert P. Nørsett
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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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Numerical solution of stiff systems of differential equations arising from chemical reactions [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2014 Long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region.
Gholamreza Hojjati +3 more
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Second Derivative Block Hybrid Methods for the Numerical Integration of Differential Systems
Fractal and Fractional, 2022 The second derivative block hybrid method for the continuous integration of differential systems within the interval of integration was derived. The second derivative block hybrid method maintained the stability properties of the Runge–Kutta methods ...
Dauda Gulibur Yakubu +3 more
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Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems [PDF]
Analysis and Applications, 2019 In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network (DNN), whose ...
C. Reisinger, Yufei Zhang
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