Approximation of Differential Equations
I. Polygonal Method
Worksheet 4 of 4:
1. Step-by-step construction: [url]http://www.geogebratube.org/material/show/id/27865[/url]
2. Transfer the procedure to the Spreadsheet view: [url]http://www.geogebratube.org/material/show/id/27754[/url]
3. Improvement: add a term in the Taylor expansion: [url]http://www.geogebratube.org/material/show/id/29108[/url]
[b]*4. Comparison of formulas:[/b]
-vary h
-choose two or three terms from the Taylor expansion.
-correction formula (following Tenenbaum and Pollard, [i]Ordinary Differential Equations[/i], Lesson 44)
Additional free parameters:
-constant coefficients in the differential equation
-initial values
I have also included a direction field
____
These materials are self-instructional. If they can be of use to you, let me know how to make them better. I have not explained the error calculation or the formulas I made for the lists of points. I am happy to fill in this missing information if it will be of use. Also, if my methods are slow and klunky, tell me!
