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5-005-StiffDifferentialEquations-TechniqueNarrative

Author(s): Kurt Bryan, Kurt Bryan

Keywords: Euler's method explicit methods implicit methods stiff sitffness stiff differential equation instability

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Abstract

Resource Image This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

Stiffness is a surprisingly common phenomenon. Many standard numerical methods applied to stiff systems of ODE's will either yield an unstable iteration that grows without limit, or just grind to a halt.

Stiffness is frequently a mathematical manifestation of a physical problem that has two or more very different scales for the independent variable.

There are numerical ODE methods well-suited to handling stiff systems and we illustrate these methods with examples.

The material is suitable for an introductory ODE course in which students have encountered systems of ODE's (at least, linear systems) and basic numerical methods, for example, Euler's method.

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Authors

Author(s): Kurt Bryan, Kurt Bryan

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