Streeter Pheps Equations

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Carlos Gomes
Carlos Gomes 2012-5-22
I need to do a program in Matlab with two first-order differential equations with the Streeter Phelps model. Please help me.
BOD: dL/dt=-(k1+ks)L+B
DO: d(D)/dt=k1L-k2D-P

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回答（2 个）

Matt Kindig
Matt Kindig 2012-5-22
What have you done so far? To get you started, look at the documentation for ode45 (and the other ODE solvers). The documentation gives really clear examples of how to set up your equations into the form required by the solvers. For first-order systems like this, it is almost trivial.
doc ode45
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Carlos Gomes
Carlos Gomes 2012-5-22
I need to put these two equations in Matlab by creating a Script and a Function. At the end I have to obtain a graph of these two equations. So I want you to explain me that :/

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Walter Roberson
Walter Roberson 2012-5-22
I have renamed your "D" to "Df" in order to prevent confusion with differentiation.
The Maple syntax would be
dsolve( [diff(L(t), t) = -(k1+ks)*L(t)+B, diff(Df(t), t) = k1*L(t)-k2*Df(t)-P ])
with result
Df(t) = (-k1 * k2 * C2 * (k1+ks) * exp(-t * (-k2+k1+ks)) + ((-P * ks + (B-P) * k1) * exp(k2*t) + C1 * k2 * (k1+ks)) * (-k2+k1+ks)) * exp(-k2*t) / ((k1+ks) * k2 * (-k2+k1+ks))
L(t) = B / (k1+ks) + exp(-(k1+ks) * t) * C2
In the above, C1 and C2 are constants of integration
  2 个评论
Carlos Gomes
Carlos Gomes 2012-5-22
I need to put these two equations in Matlab by creating a Script and a Function. At the end I have to obtain a graph of these two equations. So I want you to explain me that :/
Walter Roberson
Walter Roberson 2012-5-22
http://www.mathworks.com/matlabcentral/answers/8026-best-way-s-to-master-matlab

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