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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.

jessupj
on 28 Jan 2021

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

jessupj
on 28 Jan 2021

Edited: jessupj
on 28 Jan 2021

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

Telema Harry
on 28 Jan 2021

Edited: Telema Harry
on 28 Jan 2021

Alex Sha
on 29 Jan 2021

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