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1-003-IntroNumericalMethods-TechniqueNarrative

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: analytic solution Euler's method improved Euler's method

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Abstract

Resource Image We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions and compare them to analytic solutions.

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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

Description

We try to solve differential equations analytically (i.e., obtain a closed form solution) for the most part by attempting to maneuver the equation into a position where we can ``see" an antiderivative emerge and then jump on the opportunity by integrating both sides of the differential equation.

This solution strategy, while difficult at times, offers us a nice formula with structure we can examine and it tells us where our parameters are involved.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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