Numerical Solution for a Class of Evolution Differential Equations with $p$-Laplacian and Memory

TL;DR

This paper develops a finite element method to numerically solve a class of evolution differential equations involving the p-Laplacian and memory effects, analyzing convergence and solution behaviors through MATLAB simulations.

Contribution

It introduces two stable fixed point schemes for nonlinear algebraic systems and demonstrates their effectiveness in solving complex evolution equations with memory.

Findings

Convergence of the proposed schemes is numerically verified.

Solutions exhibit asymptotic behaviors and localization effects.

The method effectively captures solution dynamics in MATLAB simulations.

Abstract

In this paper we make a study of a partial integral differential equation with $p$-Laplacian using a mixed finite element method. Two stable and convergent fixed point schemes are proposed to solve the nonlinear algebraic system. Using the implementation of the method in Matlab environment, we numerically analyse the convergence with an example. Some other examples are presented in order to illustrate several asymptotic behaviours and some localization effects of the solutions.