Needing help using ode15s to solve an equation.

Hi there just needing some help using ode15s. I've never used this built-in function, but i need to use it to solve the equation below using ode15s:

I have the choice of what values to give the parameters, but i just dont know how to start coding. Has anyone got any tips to help me get started and complete this. Any suggestions or help is appreciated.

Answer 1

[Star Strider]

I find it easiest to let the Symbolic Math Toolbox do all the heavy lifting —

syms C(t) C_in C_0 Q_in Q_out t V_0 Y 
DE = (V_0 + (Q_in - Q_out)*t) * diff(C) + Q_in * C == Q_in * C_in

DE(t) = 

DE = isolate(DE, diff(C))

DE = 

VF = odeToVectorField(DE)

VF = 

DEfcn = matlabFunction(VF, 'Vars',{t,Y,C_in,Q_in,Q_out,V_0})        % Use This Result With The Numeric ODE Solvers

DEfcn = function_handle with value:
    @(t,Y,C_in,Q_in,Q_out,V_0)[-(Q_in.*Y(1)-C_in.*Q_in)./(V_0+t.*(Q_in-Q_out))]

C(t) = dsolve(DE, C(0) == C_0)                                      % Analytic Solution

C(t) = 

You can use matlabFunction with the right-hand-side of ‘C(t)’ to check the result of the numerical integration. Remember to include ‘C_0’ in the 'Vars' list.

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[Ryan Marsh]

Thank you very much!!!

[Star Strider]

As always, my pleasure!

[Ryan Marsh]

Just quickly, since you have been a massive help, would you also know what would be the best way to create a simple plot to show concentraion over time. Thanks :)

[Star Strider]

Thank you!

Yes!

The numerical ODE solvers are coded as:

[t,y] = ode15s( ... );

so to plot the results:

figure

plot(t,y)

grid

xlabel('Time')

ylabel('C(t)')

Since there is only one output, so only one column in ‘y’, no legend would be necessary. However it would be if several different vectors were plotted in the same axes for different parameter values, using a loop and the hold function.

.

[Ryan Marsh]

Thank you !!!

[Star Strider]

As always, my pleasure!