Effective numerical computation of $p(x)-$Laplace equations in 2D

TL;DR

This paper presents an efficient MATLAB implementation for solving 2D nonlinear elliptic equations involving the p(x)-Laplacian operator using a decomposition-coordination iterative method.

Contribution

The paper introduces a novel implementation of the decomposition-coordination method specifically for p(x)-Laplacian equations in 2D, enhancing computational efficiency.

Findings

The method efficiently solves nonlinear elliptic problems with nonstandard growth.

Implementation demonstrates high computational efficiency in MATLAB.

Applicable to a class of p(x)-Laplacian problems in 2D.

Abstract

In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the $p(x)-$Laplacian operator. Our implementation is based in the {\em decomposition--coordination} method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in {\sc MatLab} in 2 dimensions and turns out to be extremely efficient from the computational point of view.