Inverse reconstruction from images is a central problem in many scientific and engineering
disciplines. Recent progress on differentiable rendering has led to methods that can …

In this the window of the Sobolev gradient technique to the problem of minimizing a
Schrödinger functional associated with a nonlinear Schrödinger equation. We show that …

Mahavier and Montgomery construct a Sobolev space for approximate solution of linear
initial value problems in a finite difference setting in single-iteration sobolev descent for …

Approximating time evolution related to Ginzburg–Landau functionals via Sobolev gradient
methods in a finite-element setting - ScienceDirect Skip to main contentSkip to article Elsevier …

The Sobolev gradient technique has been discussed previously in this journal as an efficient
method for finding energy minima of certain Ginzburg–Landau type functionals [S. Sial, J …

To find the minima of an energy functional, is a well known problem in physics and
engineering. Sobolev gradients have proven to be affective to find the critical points of a …

The nonlinear Klein‐Gordon equation (KGE) models many nonlinear phenomena. In this
paper, we propose a scheme for numerical approximation of solutions of the one …

Sobolev gradients have been discussed in Sial et al.(2003) as a method for energy
minimization related to Ginzburg–Landau functionals. In this article, a weighted Sobolev …

The Sobolev gradient method has been shown to be effective at constructing finite-
dimensional approximations to solutions of initial-value problems. Here we show that the …

A numerical procedure for solving a class of integro-differential equations of Volterra type
using the Sobolev gradient method is presented. Results are compared with those from the …