Download presentation

Presentation is loading. Please wait.

Published byKallie Bardell Modified over 2 years ago

1
Looking for insight in the special case of antiderivatives

2
Turning Corners (or Not!!!) Euler’s method is very bad at turning corners. Think about a solution curve like this one...

3
Turning Corners (or Not!!!) Euler’s method is very bad at turning corners. When the curve nears a maximum, Euler’s method “overshoots.” Likewise, when the curve nears a minimum, Euler’s method drops too far.

4
Point of View tt tt When our differential equation is of the form Euler’s method is a generalization of the left end-point Riemann sum! y = slope t = f’(t) tArea = f’(t) t

5
Midpoint Approximations tt The midpoint Riemann sum is much more accurate. tt tt We use this insight to improve on Euler’s method.

6
Improved Euler’s Method The idea obviously has merit. There’s only one problem... We don’t know the value of the function at the midpoint. We only know the value of the function at the left endpoint. But we can approximate the value of the function at the midpoint using the ordinary Euler approximation! tt tt

7
Here it is! Old t and Old y temp t = Old t + 0.5( t) Temp y = Old y + 0.5( t) y’(Old t, Old y) New t = Old t + t New y = Old y + y’(Temp t, Temp y) t

Similar presentations

OK

Euler’s Method Building the function from the derivative.

Euler’s Method Building the function from the derivative.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on identity property of multiplication Ppt on fdi in indian retail sector Economics ppt on demand and supply Ppt on new zealand culture in the 19th Immune system for kids ppt on batteries Ppt on world wide web Ppt on mpeg audio compression and decompression software Difference between lcd and led display ppt on tv Ppt on nitrogen cycle and nitrogen fixation by lightning Ppt on 555 timer oscillator