A note about high-order semi-implicit differentiation: application to a numerical integration scheme with Taylor-based compensated error

TL;DR

This paper introduces a third-order semi-implicit differentiator that enhances a Taylor-based numerical integration scheme, offering improved convergence and real-time implementation flexibility through a novel differentiation approach.

Contribution

It presents a new third-order semi-implicit differentiator that complements existing Taylor expansion methods, enabling better convergence and real-time application.

Findings

Numerical results validate the effectiveness of the proposed method.

The approach improves global convergence in numerical integration.

The method offers flexible tuning for real-time processes.

Abstract

In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor expansion refinement. The proposed algorithm is dual to the interconnected approach since it offers alternative flexibility to be tuned and to be implemented in real-time processes. In particular, an application to a numerical integration scheme is presented as the Taylor refinement can be of interest to improve the global convergence. Numerical results are presented to support the rightness of the proposed method.