Second oder ode solution with euler methods

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Bayram FURKAN TORA
评论： James Tursa 2020-3-12
??̈+ ??̇ + ?? = ???(??) where, ?(? = ?) = ? and ?̇(? = ?) = 2 ? values in the domain of [? ??]. with a step size of ?? = ?. ?. How can I solve this system using euler methods ?
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Erivelton Gualter
Erivelton Gualter 2019-5-1
Hello Bayram,
You can easily use the ODE solvers from Matlab. Check the link bellow:
https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html
Also, you can write your own method. Check the follow link:
http://tutorial.math.lamar.edu/Classes/DE/EulersMethod.aspx
Try to implement it and if you face a problem, share here your code and I will be glad to help.

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回答（1 个）

James Tursa
James Tursa 2019-5-1
编辑：James Tursa 2019-5-2
Rewrite your 2nd order equation as a pair of first order equations, then use Euler method on a 2-element vector. I.e.,
Define your 2-element state vector y as
y(1) is defined to be x
y(2) is defined to be xdot
The derivative of y(1) is y(2) by definition.
The derivative of y(2) can be found by solving your 2nd order DE for xdotdot.
See the van der Pol equation example in the doc here for an example of turning a 2nd order DE into a pair of 1st order DEs:
https://www.mathworks.com/help/matlab/ref/ode45.html?searchHighlight=ode45&s_tid=doc_srchtitle
You can essentially use your 1st order Euler code as an outline for this 2nd order system. Simply replace the scalar state with a 2-element vector state in your code.
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Pranay Harjai
Pranay Harjai 2020-3-12
How to replace the scalar state with a 2-element vector state
James Tursa
James Tursa 2020-3-12
Open up a new question, show your current code, and then we can show you how to modify it for a 2-element state vector.

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