Results 91 to 100 of about 13,068 (272)

A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs

Journal of Applied Mathematics, 2019
In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered.
I. B. Aiguobasimwin, R. I. Okuonghae
doaj   +1 more source

Capturing Complex Rate‐Dependent Behaviors of Saturated Clays: A Fractional Consistency Kinematic Hardening Viscoplastic Approach

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper ...
Wei Cheng, Zhen‐Yu Yin
wiley   +1 more source

Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems

Abstract and Applied Analysis, 2013
We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and ...
S. Z. Ahmad, F. Ismail, N. Senu, M. Suleiman   +3 more
doaj   +1 more source

Systematic Parameter Selection for Short Fiber Polymer Composite Direct Fiber Simulation

Polymer Composites, EarlyView.
Interactions of individually simulated fibers are systematically calibrated such that their orientation history agrees with the results from analytical orientation models. ABSTRACT The orientation of fibers in short discontinuous fiber reinforced polymer composites is a critical factor in determining final mechanical and thermal properties.
Jason B. Pierce, Douglas E. Smith
wiley   +1 more source

Some Practical Runge-Kutta Formulas [PDF]

Mathematics of Computation, 1986
A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation.
openaire   +2 more sources

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Propellants, Explosives, Pyrotechnics, EarlyView.
Physics‐Aware Recurrent Convolutional Neural Networks (PARC) can reliably learn the thermomechanics of energetic materials as a function of morphology. This work introduces LatentPARC, which accelerates PARC by modeling the dynamics in a low‐dimensional latent space.
Zoë J. Gray, Joseph B. Choi, Youngsoo Choi, H. Keo Springer, H. S. Udaykumar, Stephen S. Baek   +5 more
wiley   +1 more source

Lie Group Method of the Diffusion Equations

Advances in Mathematical Physics, 2014
The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. Numerical results showed that Lie
Jian-Qiang Sun, Rong-Fang Huang, Xiao-Yan Gu, Ling Yu   +3 more
doaj   +1 more source

Runge–Kutta methods and renormalization [PDF]

The European Physical Journal C, 2000
A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher's group and B-series are shown to provide a suitable framework for renormalizing a toy model of field the ory, following Kreimer's approach.
openaire   +2 more sources

Impact of small‐scale gravity waves on tracer transport

Quarterly Journal of the Royal Meteorological Society, EarlyView.
We extend a gravity wave (GW) parametrization to calculate the tracer transport due to the GW–Stokes drift and next‐order effects, where the approach is validated by comparing coarse‐resolution simulations with parametrized GWs to high‐resolution, wave‐resolving reference simulations.
Irmgard Knop, Stamen Dolaptchiev, Ulrich Achatz   +2 more
wiley   +1 more source

Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Mathematics
In this paper, we develop explicit three-derivative two-step Runge–Kutta (ThDTSRK) schemes, and propose a simpler general form of the order accuracy conditions (p≤7) by Albrecht’s approach, compared to the order conditions in terms of rooted trees.
Xueyu Qin, Jian Yu, Chao Yan
doaj   +1 more source