A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme

TL;DR

This paper analyzes the convergence properties of a newly proposed diffusive representation-based numerical scheme for fractional derivatives, emphasizing its efficiency and potential for accurate computation.

Contribution

It provides a systematic convergence analysis of a novel, fast, and memory-efficient numerical method for fractional derivatives based on diffusive representation.

Findings

The scheme exhibits good convergence properties.

The method is computationally efficient and memory-friendly.

The analysis confirms the method's suitability for practical applications.

Abstract

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory efficient. Moreover, the method's design is such that good convergence properties may be expected. This paper here starts a systematic investigation of these convergence properties.