Numerical differentiation in time in function used by ODE

6 次查看（过去 30 天）
Mithrandir
Mithrandir 2023-10-13
评论： Mithrandir 2023-10-13
Hi all, I'm working on a code that uses an ODE integration instead of a Runge - Kutta method (4th order).
By now I'm trying to see if it's possibile to numerically differentiate in time a variable calculated inside a function that is then given as an input to ODE. Essentially my function will compute values at single instants as time proceeds and for this reason I can't define an array on which I can compute a numerical differentiation with diff function.
I'm attaching an image of the full equation:
The variable I want to differentiate numerically is .
Thanks in advance.
  6 个评论
显示 4更早的评论
Torsten
Torsten 2023-10-13
Do you want to differentiate rho_l or rho_l_dot with respect to time ? You wrote you want to differentiate rho_l_dot again to get rho_l_doubledot. But maybe that was wrong ?
Mithrandir
Mithrandir 2023-10-13
@Torsten Only rho_l since no second derivative will be needed. Sorry for stating it wrong.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Torsten
Torsten 2023-10-13
编辑：Torsten 2023-10-13
ode15s can solve systems of differential equations of the form M*y' = f(t,y) where M is the so called mass matrix. If a row j of this matrix is zero, the corresponding equation reads 0 = f_j(t,y) , thus is an algebraic equation.
In your case, define a new algebraic solution variable v as v = rho_l and add the algebraic equation v - rho_l = 0 to your system of differential-algebraic equations to be solved. If you now have to use dv/dt (= drho_l/dt) somewhere in your code, you can include it in your computations by setting a coefficient different from 0 in the mass matrix M of the system in the column that corresponds to v .
  3 个评论
显示 1更早的评论
Torsten
Torsten 2023-10-13
编辑：Torsten 2023-10-13
I adjusted the answer for that you want rho_l_dot, not rho_l_doubledot.
And you should start with a simple test example to see how it works to implicitly get the time derivative of an algebraic variable in the way I described.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Numeric Solvers 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by