An approximate proximal numerical procedure concerning the generalized method of lines

TL;DR

This paper introduces an approximate proximal numerical method for the generalized method of lines, extending previous work to improve the discretization and solution of PDEs along lines or curves.

Contribution

It presents a novel approximate proximal approach tailored for the generalized method of lines, enhancing its applicability and computational efficiency.

Findings

Extended previous methods with new proximal approach

Improved discretization for PDEs along lines or curves

Demonstrated effectiveness through applications

Abstract

This article develops an approximate proximal approach for the generalized method of lines. The present results are extensions and applications of previous ones which have been published since 2011, in books and articles such as [3,4,5,6]. We also recall that in 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.