Analyzing the absolute stability region of implicit methods of solving ODEs
Mihail Semenov
TL;DR
This paper reviews implicit methods for solving stiff ODEs, focusing on the absolute stability regions of Gear's methods, and provides guidance on selecting the appropriate order for these methods.
Contribution
It introduces a graphical analysis of the absolute stability regions for Gear's methods and offers recommendations for choosing the method order.
Findings
Graphical representation of stability regions for Gear's methods
Guidelines for selecting the optimal order of Gear's methods
Enhanced understanding of stability properties for stiff ODE integration
Abstract
Review of implicit methods of integrating system of stiff ordinary differential equations is presented. Defines and graphically presents absolute stability region for Gears methods (backward differentiation formula) used to solve system of stiff ordinary differential equations. Recommendations for selecting the order of Gears method are given.
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Taxonomy
TopicsNumerical methods for differential equations · Iterative Learning Control Systems · Mechanical Systems and Engineering