# Optimization of One-parameter Family of Integration Formulae for Solving Stiff Chemical-kinetic ODEs

Source: [Optimization of One-parameter Family of Integration Formulae for Solving Stiff Chemical-kinetic ODEs](<https://www.sota2.com/research/paper/68fa3abf1e209131ce8cd3f1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:14:45.583Z

Authors: Youhi Morii, Eiji Shima

Published: 2019-10-12T14:27:11.000Z

## Abstract

A fast and robust Jacobian-free time-integration method - called Minimum-error Adaptation of a Chemical-Kinetic ODE Solver (MACKS) - for solving stiff ODEs pertaining to chemical-kinetics is proposed herein. The MACKS formulation is based on optimization of the one-parameter family of integration formulae coupled with a dual time-stepping method to facilitate error minimization. The proposed method demonstrates higher accuracy compared to the method - Extended Robustness-enhanced numerical algorithm (ERENA) - previously proposed by the authors. Additionally, when this method is employed in homogeneous-ignition simulations, it facilitates realization of faster performance compared to the Variable-coefficient ODE solver (VODE).

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1910.05567>)

[PDF](<https://arxiv.org/pdf/1910.05567.pdf>)