Runge-kutta methods - Open Access .click

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Approximating High-Order Adversarial Attacks Using Runge−Kutta Methods

Tsinghua Science and Technology
Adversarial attacks craft adversarial examples (AEs) to fool convolution neural networks. The mainstream gradient-based attacks, based on first-order optimization methods, encounter bottlenecks to generate high transferable AEs attacking unknown models ...
Anjie Peng +4 more
doaj +1 more source

Semiexplicit 𝐴-stable Runge-Kutta methods [PDF]

Mathematics of Computation, 1979
An s − 1 ...
Cooper, G. J., Sayfy, A.
openaire +1 more source

Learning regime‐dependent governing equations: A symbolic decision tree approach

AIChE Journal, EarlyView.
Abstract Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data‐driven discovery of regime‐dependent governing equations essential for predictive modeling, optimization, and control. We propose symbolic decision trees for the data‐driven discovery of regime‐dependent governing equations.
Ilias Mitrai, Tongjia Liu, Gabriel E. Sanoja +2 more
wiley +1 more source

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

, 1996
The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations.
Burrage, Pamela +3 more
core +1 more source

Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise [PDF]

, 2012
In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM (s,r) methods to construct symplectic Runge–Kutta methods for all values of s and r with s≥r.
Burrage, Pamela, Burrage, Pamela M., Burrage, Kevin +2 more
core +2 more sources

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

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

Mixed collocation methods for y” = f(x , y) [PDF]

, 1999
The second-order initial value problem y" = f(x,y), y(x(_0)) = y(_0), y'(x(_0)) = z(_0) which does not contain the first derivative explicitly and where the solution is oscillatory has been of great interest for many years.
Duxbury, S.C., Duxbury, Suzanne Claire
core

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, Kent-Andre Mardal, Trygve K. Nilssen +2 more
doaj +1 more source

On Multisymplecticity of Partitioned Runge–Kutta Methods [PDF]

SIAM Journal on Scientific Computing, 2008
Previously, it has been shown that discretizing a multi-Hamiltonian PDE in space and time with partitioned Runge-Kutta methods gives rise to a system of equations that formally satisfy a discrete multisymplectic conservation law. However, these previous studies use the same partitioning of the variables into two parts in both space and time. This gives
Brett N. Ryland, Robert I. McLachlan
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mathematics
runge–kutta methods
order conditions

stochastic differential equations
numerical integration