Calculation of Univariate Pade Approximants for solutions of the Michaelis-Menten equation with first order input using the Tau method

TL;DR

This paper introduces a recursive approach using the Jacobi formula and the Tau method to compute univariate Pade approximants for solutions of the Michaelis-Menten equation with first order input, emphasizing pattern-based cancellations.

Contribution

It presents a novel recursive algorithm leveraging the Jacobi formula and Tau method for efficient computation of Pade approximants in enzyme kinetics modeling.

Findings

Efficient recursive computation of Pade approximants

Pattern-based cancellations improve algorithm stability

Application to Michaelis-Menten equation solutions

Abstract

In this paper the Jacobi formula is used to recursively generate (diagonal) univariate Pade approximants using the Tau method for solutions Michaelis-Menten equation with first order input. In the algorithm the Jacobi coefficients and error terms in the Tau method are postulated to have a particular form, and this form is maintained by specific patterns of cancellations.