Journal of Advances in Applied Mathematics

JAAM
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Volume 5, Number 1, January 2020

A Class of Stable Algorithms for Stiff Ordinary Differential Equation System
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KB)PP.
26-34

, Pub. Date:December 12, 2019
DOI:

10.22606/jaam.2020.51004
**Author(s)**
Ying-Qiu Gu

**Affiliation(s)**
School of Mathematical Science, Fudan University, Shanghai 200433, China

**Abstract**
In this paper, we introduce a series of stable algorithms for solving the stiff ordinary
differential equation system. These algorithms are based on the solution to the local linearized
perturbation equation and Padé approximations of exponential function. The algorithms get rid
of the influence of the stiffness and have explicit schemes. In contrast with conventional implicit
schemes, this class of schemes has some advantages such as the simple program code, high precision,
good convergence and strong stability by the virtue of Padé approximation. It is a good assistant
for the researchers unfamiliar with the numerical analysis theory.

**Keywords**
Stiff ordinary differential equation system, Padé approximant, stable algorithm, explicit
algorithm

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