Results 61 to 70 of about 76,470 (160)

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

A Variational Problem and Classification Theorem for Extremal Hypersurfaces in the Space Form

Journal of Mathematics, 2022
The classification of the isoparametric extremal hypersurfaces in the space form is obtained in this paper. We also derived the Euler-Lagrange equation for extremal hypersurface and obtained Simons’ type integral inequality.
Yu-Chung Chang
doaj   +1 more source

The Herglotz variational problem on spheres and its optimal control approach [PDF]

, 2016
The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation ...
Abrunheiro, Lígia, Machado, Luís, Martins, Natália   +2 more
core  

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

, 2010
We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted
A.B. Malinowska, A.C. Chiang, Agnieszka B. Malinowska, B. Beavis, C.C. Von Weiszacker, D. Cai, D. Gale, D. Kravvaritis, Delfim F. M. Torres, F. Giannessi, F. Ramsey, F.M. Atici, F.M. Atici, F.M. Atici, I.E. Schochetman, M. Bohner, M. Bohner, M. Bohner, M. Bohner, N. Martins, Natália Martins, P. Michel, P.M. Pardalos, P.S. Dasgupta, R. Almeida, R. Okomura, S. Lang, T. Kamihigashi, W.A. Brock, Z. Bartosiewicz   +29 more
core   +1 more source

Analytical Solutions for the Cardiac Extracellular‐Membrane‐Intracellular Model

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The cardiac extracellular‐membrane‐intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The cardiac EMI model provides a more detailed description of the heart's electrical activity compared to traditional monodomain and bidomain models, potentially making it better‐suited for understanding the
Carlos Ballesteros, Alexei Cheviakov, Raymond J. Spiteri   +2 more
wiley   +1 more source

Stochastic fiber dynamics in a spatially semi-discrete setting

, 2016
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model for which no solution theory is available, it consists of a high ...
Lindner, Felix, Marheineke, Nicole, Stroot, Holger, Vibe, Alexander, Wegener, Raimund   +4 more
core   +1 more source

Dynamics Modeling of Robot Manipulators Based on Deep Lagrangian Network and Torque Separation Technique

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT In recent years, learning robot manipulator dynamics with deep networks has been extensively studied, as it avoids deriving the analytical expression of the robot dynamics equations. In particular, deep Lagrangian networks that incorporate the prior knowledge of Lagrangian mechanics into the deep networks have shown prominent advantages in ...
Xianglong Liang, Tianyu Gao, Zhikai Yao, Jianyong Yao   +3 more
wiley   +1 more source

Dynamic Modeling and Simulation of Morphing Wing Aircraft Considering Rigid‐Elastic Coupling Effects

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT During the morphing process, the dynamic modeling of the morphing wing aircraft presents the characteristics of rigid‐elastic coupling effects, moving boundaries, and low computational efficiency. Meanwhile, parameters such as aerodynamic forces/moments, center of pressure, center of mass, and moment of inertia would also change significantly,
Xu Zha, Boran Qiao, Yingpeng Zhuo, Chengze Zhao, Yuchen Yang, Lixin Guan   +5 more
wiley   +1 more source

Elastoplasticity Informed Kolmogorov–Arnold Networks Using Chebyshev Polynomials

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Multilayer perceptron (MLP) networks are predominantly used to develop data‐driven constitutive models for granular materials. They offer a compelling alternative to traditional physics‐based constitutive models in predicting non‐linear responses of these materials, for example, elastoplasticity, under various loading conditions. To attain the
Farinaz Mostajeran, Salah A. Faroughi
wiley   +1 more source