How to solve a systems of ODE and Algebraic Equations
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I have a system of 3 nonlinear ODE and 2 nonlinear algebraic equations.
Please how can I solve these systems of equation.
ODE 45 can easily solve the ODE part. However, I don't know how to combine the solution from ODE45 and the algebraic equations.
Thank you.
2 件のコメント
jessupj
2021 年 1 月 28 日
編集済み: jessupj
2021 年 1 月 28 日
it sounds like what you're after is "how to solve a DAE" if the algebraic eqations constrain the solutions of the ODE part https://www.mathworks.com/help/matlab/math/solve-differential-algebraic-equations-daes.html
otherwise, if the algebraic equations aren't constraints (ie. they determine diagnostic variables), you probably want to solve the ODE and then solve the algebraic equations 'offline' using e.g. fsolve
採用された回答
jessupj
2021 年 1 月 28 日
編集済み: jessupj
2021 年 1 月 28 日
looks like you've got a non-autonomous DAE.
with u=x(4) and y = x(5), you'd have:
dx(1) = -wh.*x(1) + wh.* x(5)
dx(2) = -wl.*x(2) + A.*sin(w.*t).* wl.*(x(5) - x(1))
dx(3) = K.*x(2)
0 = x(3) + A.* sin(w.*t) - x(4)
0 = 25 - (5 - x(4) ).^2 - x(5) % = 25 - (25 -10*x4 + x4^2) -x5 = x4*(10 -x4)-x5
and check this old post:
https://www.mathworks.com/matlabcentral/answers/360710-how-to-solve-a-set-of-odes-and-a-nonlinear-equation
その他の回答 (1 件)
Telema Harry
2021 年 1 月 28 日
編集済み: Telema Harry
2021 年 1 月 28 日
2 件のコメント
Alex Sha
2021 年 1 月 29 日
Hi, since: u = x(3) + A.* sin(w.*t) and y = 25 - (5 - u).^2, so y = 25 - (5 - ( x(3) + A.* sin(w.*t))).^2, substitute y into dx1dt and dx2dt, then pure ODE functions will be formed.
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