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6-002-EulerCromerPendulum-ModelingScenario

Author(s): Eddie Fuselier

High Point University, High Point, NC USA

Keywords: pendulum semi-implicit methods Euler-Cromer numerical solvers

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Abstract

Resource Image This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.

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

Description

Experimental observations (some of them surprising!) should lead to discussions about computational accuracy, stability, and efficiency.

When using a numerical method to model physical phenomena, we are often interested in observing the solution's behavior in the long run. Planetary motion and fluid flow are examples of applications where this might be important. If the numerical solution is ``well-behaved'' over time, we say it is stable. This idea can be made precise, but this informal notion will suffice for now. Of course we are also interested in accuracy and efficiency - i.e., we'd like to obtain a reasonable simulation in as few computations as possible, especially when pressed for computational resources.

 

 

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Authors

Author(s): Eddie Fuselier

High Point University, High Point, NC USA

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