Can ode45 solve a ODE with space dependent parameters?

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Marlon Saveri Silva 2019-1-28

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评论： James Tursa 2021-8-5

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Hello,

I read ode45() can solve functions with time dependent parameters like this below by interpolating f and g during each time step.

y'(t)+f(t)y(t)=g(t)

However, can ode45 (or other solver) solve a system of odes like this below in which [A], [B] and [C] are matrices with some terms dependent of y and y=y(t)?

{dy/dt} = [A]{y^4}+[B]{y}+{C}
Ai=Ai(y)
Bi=Bi(y)
Ci=Ci(y)

Well, since this equation appears in a problem I solve using Simscape (Backward Euler method as default), I suppose I could find a solver to solve it inside Matlab codes without using Simscape.

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Jan 2019-1-29

The notation is not clear to me: "{dy/dt} = [A]{y^4}+[B]{y}+{C}"

Marlon Saveri Silva 2019-1-29

编辑：Marlon Saveri Silva 2019-1-29

Actually this is not a MATLAB command line notation, I tried this "mathematical notation" to emphasize y, dy/dt and C are vectors whereas A and B are matrices.

{y} = {y1, y2, y3, ... , yn}

{C} = {c1, c2, c3, ... , cn}

{dy/dt} = {y1', y2', y3', ... , yn'}

Moreover, by {y^4} I tried to indicate the vector is {y1^4, y2^4, y3^4, ... yn^4}.

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采纳的回答

James Tursa 2019-1-29

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https://ww2.mathworks.cn/matlabcentral/answers/441958-can-ode45-solve-a-ode-with-space-dependent-parameters#answer_358549

Yes. In general, if the derivative is a function of current state and time (even if there are vectors or matrices involved), then you can use ode45 to get a numerical solution. The caveat is that the function needs to be "nice" enough for ode45 to handle. Otherwise you may need stiff solvers, etc.

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Ying Wu 2021-8-5

Hi Silva, I have met the same problem, my ODE has parameter A which is the piecewise function of the first directive y'(t). Have you succeed in solving this problem?