Results 91 to 100 of about 3,089 (203)

Differential-integral Euler-Lagrange equations

Iranian Journal of Numerical Analysis and Optimization
Summary: In this paper, we will study the calculus of variations problem in the presence of a system of differential-integral equations. In order to identify the necessary optimality conditions for this problem, we will derive the so-called differential-integral(D-I) Euler-Lagrange equations. We will also generalize this problem to other cases, such as
openaire   +3 more sources

The Optimal Mean–Variance Selling Problem With Finite Horizon

Mathematical Finance, EarlyView.
ABSTRACT The optimal mean–variance selling problem seeks to determine a dynamically optimal stopping time in the nonlinear problem sup0≤τ≤TE(Xτ)−cVar(Xτ)$\sup _{0 \le \tau \le T} \left[ \mathsf {E}\,\!(X_\tau) - c\, \mathsf {V}ar\,\!(X_\tau) \right]$, where X$X$ is a geometric Brownian motion with strictly positive drift, the supremum is taken over ...
Peter Johnson, Jesper Lund Pedersen, Goran Peskir   +2 more
wiley   +1 more source

Solution of the KdV equation with fractional time derivative via variational method

Electronic Journal of Differential Equations, 2014
This article presents a formulation of the time-fractional generalized Korteweg-de Vries (KdV) equation using the Euler-Lagrange variational technique in the Riemann-Liouville derivative sense. It finds an approximate solitary wave solution, and shows
Youwei Zhang
doaj  

Accelerated Interior Point Algorithms for Rate‐Independent Single Crystal Plasticity at Small Strains

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Rate‐independent single crystal plasticity requires robust solution methods due to the non‐uniqueness of slip system activity. The interior point method, which enforces the yield criterion via slack variables and a so‐called barrier term, has proven both robust and computationally efficient for this class of problems and has been applied to ...
Felix Steinmetz, Lisa Scheunemann
wiley   +1 more source

The Long Shadow of Karl Weierstraß Over the Calculus of Variations

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT At first glance, it appears that the contents of Karl Weierstraß's (1815–1897) lecture courses on the calculus of variations were made available to the public only in the seventh volume of his Mathematische Werke, and thus not until 30 years after his death.
Peter Ullrich
wiley   +1 more source

Optimizing Variational Problems through Weighted Fractional Derivatives

Fractal and Fractional
In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with
Ricardo Almeida
doaj   +1 more source

Accurate and Efficient Data‐Driven Partitioned Scheme for Coupled Heterogeneous Numerical Models

Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.
ABSTRACT Heterogeneous numerical models (HNMs) combine conventional discretization modules such as finite elements with nonconventional data‐driven and reduced‐order modules. HNMs can improve computational efficiency and enable simulations of multi‐physics systems in which one or more constituent components lack first‐principles descriptions and must ...
Edward Huynh, Justin Owen, Paul Kuberry, Pavel Bochev   +3 more
wiley   +1 more source

Global solutions to a one-dimensional nonlinear wave equation derivable from a variational principle

Electronic Journal of Differential Equations, 2017
This article focuses on a one-dimensional nonlinear wave equation which is the Euler-Lagrange equation of a variational principle whose Lagrangian density involves linear terms and zero term as well as quadratic terms in derivatives of the field.
Yanbo Hu, Guodong Wang
doaj  

Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.
ABSTRACT To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of
Andres Ortegón‐Villacorte, Jan Rohleff   +1 more
wiley   +1 more source

Adaptive Matrix‐Free Simulations of Fluid‐Filled Phase‐Field Fractures With Fixed‐Stress Coupling and Fracture‐Width Computation

International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.
ABSTRACT Fluid‐filled phase‐field fracture simulations require robust, scalable solvers that can handle strongly nonlinear, non‐smooth mechanics and tightly coupled flow on locally refined meshes. In this work, we develop an adaptive finite element framework for quasi‐static, fluid‐filled phase‐field fractures that combines semi‐smooth Newton methods ...
Leon M. Kolditz, Viktor Kosin, Sanghyun Lee, Thomas Wick   +3 more
wiley   +1 more source