How do you work out if Euler's method overestimates the actual solution, for the ODE:

Brunton39

Brunton39

Answered question

2022-06-21

How do you work out if Euler's method overestimates the actual solution, for the ODE:
d y d x = 24 tan ( π x )
With steps of 0.25 from 1 x 2?

Answer & Explanation

Josie123

Josie123

Beginner2022-06-22Added 16 answers

d y = 24 tan ( π x ) d x y ( x ) = 24 tan ( π x ) d x 24 π tan ( u ) d u = 24 π s i n ( u ) c o s ( u )
Let s = cos ( u ) then d s = sin ( u ) d u so you get :
24 π 1 s d s = 24 π ln ( s ) + c
Substitute s back in and you get :
24 π ln ( s ) + c = 24 π ln ( c o s ( π x ) ) + c
Now you can evaluate anything you want.

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