Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials

TL;DR

This paper explores efficient numerical methods for solving fractional differential equations in viscoelastic material modeling, addressing computational challenges through infinite state representations and parameter optimization based on numerical experiments.

Contribution

It introduces improved solution algorithms using infinite state representations and provides guidance on parameter selection to enhance computational efficiency.

Findings

Effective parameter choices for infinite state algorithms

Reduced computational complexity in fractional differential equations

Enhanced modeling accuracy for viscoelastic materials

Abstract

Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional differential operators, in particular regarding the high computational complexity and the high memory requirements. The infinite state representation is an approach on which one can base numerical methods that overcome these obstacles. Such algorithms contain a number of parameters that influence the final result in nontrivial ways. Based on numerical experiments, we initiate a study leading to good choices of these parameters.