Solving Differential Equations in R: Package deSolve
Journal of Statistical Software, 2010 In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved ...
Karline Soetaert +2 more
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Solution of nonlinear stiff differential equations for a three-phase no-load transformer using a Runge–Kutta implicit method [PDF]
Archives of Electrical Engineering, 2022 The paper presents an approach to differential equation solutions for the stiff problem. The method of using the classic transformer model to study nonlinear steady states and to determine the current pulses appearing when the transformer is turned on is
Bernard Baron +4 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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Schur Decomposition for Stiff Differential Equations
CoRR, 2023 A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially when the time step is adapted to maintain a prescribed local error.
Thoma Zoto, John C. Bowman
openaire +2 more sources
IEEE Access, 2022 The modeling and simulation of fluid power systems are essential parts of the real-time simulation of virtual prototypes of mobile working machines.
Stanislav Ustinov +2 more
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An efficient numerical algorithm for the transient analysis of high-frequency non-linear circuits [PDF]
, 2002 The paper proposes a new approach for the discrete-time integration of non-linear differential equations that describe the behaviour of high-frequency circuits, in particular those containing complex equivalent-circuit models of microwave transistor ...
Condon, Marissa +5 more
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Explicit Stabilized Multirate Method For Stiff Differential Equations [PDF]
, 2022 Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit.
Grote, Marcus J. +3 more
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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
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Converting DAE models to ODE models: application to reactive Rayleigh distillation [PDF]
, 2013 This paper illustrates the application of an index reduction method to some differential algebraic equations (DAE) modelling the reactive Rayleigh distillation.
Monfreda, Fabien +3 more
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Relativistic resistive magneto-hydrodynamics code for high-energy heavy-ion collisions
European Physical Journal C: Particles and Fields, 2023 We construct a relativistic resistive magneto-hydrodynamic (RRMHD) numerical simulation code for high-energy heavy-ion collisions as a first designed code in the Milne coordinates. We split the system of differential equations into two parts, a non-stiff
Kouki Nakamura +3 more
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