An Approximate Proximal Numerical Procedure Concerning the Generalized Method of Lines

Author:

Botelho Fabio Silva

Abstract

This article develops an approximate proximal approach for the generalized method of lines. We recall that for the generalized method of lines, the domain of the partial differential equation in question is discretized in lines (or in curves) and the concerning solution is developed on these lines, as functions of the boundary conditions and the domain boundary shape. Considering such a context, in the text we develop an approximate numerical procedure of proximal nature applicable to a large class of models in physics and engineering. Finally, in the last sections, we present numerical examples and results related to a Ginzburg–Landau-type equation.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference10 articles.

1. Topics on Functional Analysis, Calculus of Variations and Duality;Botelho,2011

2. Existence of solution for the Ginzburg–Landau system, a related optimal control problem and its computation by the generalized method of lines

3. Functional Analysis and Applied Optimization in Banach Spaces;Botelho,2014

4. Functional Analysis, Calculus of Variations and Numerical Methods in Physics and Engineering;Botelho,2020

5. Sobolev Spaces;Adams,1975

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