Results 51 to 60 of about 82,462 (247)
FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs [PDF]
, 2011 FATODE is a FORTRAN library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities. The paper describes the capabilities, implementation, code organization, and usage of this package.
Sandu, Adrian, Zhang, Hong
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Fractional Order Runge-Kutta Methods
CoRR, 2022 This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total differential for Caputo fractional derivative, we construct explicit and implicit FORK methods, as the well-known Runge ...
Farideh Ghoreishi, Rezvan Ghaffari
openaire +2 more sources
AIChE Journal, EarlyView.Abstract Emulsion separation remains a persistent challenge in chemical and process industries due to the metastable nature of dispersed droplets. In gravity separators, the overall separation rate is governed by the formation of a densely packed zone (DPZ) of deforming and coalescing droplets that mediates between the dispersed and continuous phases ...
Andrei Zlobin +8 more
wiley +1 more source
Effective order strong stability preserving Runge–Kutta methods [PDF]
, 2012 We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher ...
Hadjimichael, Y. +3 more
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Semiexplicit 𝐴-stable Runge-Kutta methods [PDF]
Mathematics of Computation, 1979 An s − 1 s - 1 stage semiexplicit Runge-Kutta method is represented by an s × s s \times s real lower triangular matrix where the number of implicit stages is given by the number of nonzero diagonal elements. It is shown that the maximum order attainable is s when
Cooper, G. J., Sayfy, A.
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Predicting Performance of Hall Effect Ion Source Using Machine Learning
Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This study introduces HallNN, a machine learning tool for predicting Hall effect ion source performance using a neural network ensemble trained on data generated from numerical simulations. HallNN provides faster and more accurate predictions than numerical methods and traditional scaling laws, making it valuable for designing and optimizing Hall ...
Jaehong Park +8 more
wiley +1 more source
Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems
Mathematics, 2021 In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way.
Maria Jesus Moreta
doaj +1 more source
Equilibrium Propagation for Dissipative Dynamics
Advanced Intelligent Systems, EarlyView.This work develops local learning rules for damped linear dynamical systems, including mechanical structures and resistor‐inductor‐capacitor (RLC) circuits, by leveraging an effective action formulation. It demonstrates how physical systems can autonomously compute gradients and learn temporal patterns, enabling applications such as sound ...
Marc Berneman, Daniel Hexner
wiley +1 more source
Preconditioning of fully implicit Runge-Kutta schemes for parabolic PDEs [PDF]
Modeling, Identification and Control, 2006 Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs (9).
Gunnar A. Staff +2 more
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Another approach to Runge-Kutta methods [PDF]
, 2004 The condition equations are derived by the introduction of a system of equivalent differential equations, avoiding the usual formalism with trees and elementary differentials.
Traas, C.R.
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