ode45 function matrix dimensions problem

Hello friends I wrote a code. But this does not work. In this problem I have a parameter with range. I could not figure out how can I write. I tried something but it didn't work. I need to observe different Y_H values effects on system.

Parameter with range:

Y_H=[0.6 0.7]

CODE

clear all;

clc;

close all;

global mu_H Y_H Ks X_BH teta Ss_in

mu_Hmax=0.15; %days^-1

T=22.6; %centigrade

X_BH=2295; %mg/l

teta=1.25; %day

Y_H=[0.6 0.7];

Ks=250; %mg/l

%initial condition is Ss_in=1127 mg/l

Ss_in=1127; %mg/l

mu_H=mu_Hmax*1.072^(T-20); %day^-1

tspan=[30 32 34 36 50 52 57 59 61 63 65 72 75 76 79 83 85 87 89 96 99 106 109 116 118 121 124 125 126 127 131 133 134 135 136 137 140];

ode45(@substrate,tspan,Ss_in)

plot(t,Ss);

xlabel('Time (day)')

ylabel('Concentrations (mg/L)')

legend ('Substrate')

function Derivative = substrate (t,Ss)

global mu_H Y_H Ks X_BH teta Ss_in

Derivative = -((mu_H/Y_H)*(Ss/(Ks+Ss))*X_BH)+((1/teta)*(Ss_in-Ss)); %dSs/dt

Derivative=Derivative(:);

end

ERRORS I HAVE

Error using /

Matrix dimensions must agree.

Error in Solutionofmodeleqn31>substrate (line 26)

Derivative = -((mu_H/Y_H)*(Ss/(Ks+Ss))*X_BH)+((1/teta)*(Ss_in-Ss)); %dSs/dt

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in Solutionofmodeleqn31 (line 18)

ode45(@substrate,tspan,Ss_in)

Answer 1

[Alan Stevens]

You need to loop through the Y_H values. See below

global mu_H  Ks X_BH teta Ss_in
mu_Hmax=0.15; %days^-1
T=22.6; %centigrade
X_BH=2295; %mg/l
teta=1.25; %day
Y_H=[0.6 0.7];
Ks=250; %mg/l
%initial condition is Ss_in=1127 mg/l
Ss_in=1127; %mg/l
mu_H=mu_Hmax*1.072^(T-20); %day^-1
tspan=[30 32 34 36 50 52 57 59 61 63 65 72 75 76 79 83 85 87 89 96 99 ...
       106 109 116 118 121 124 125 126 127 131 133 134 135 136 137 140];
Ss = zeros(numel(t),numel(Y_H));
% Loop through Y_H values
for i = 1:numel(Y_H)
[t,Ss(:,i)] =ode45(@(t,Ss) substrate(t,Ss,Y_H(i)),tspan,Ss_in);
end
plot(t,Ss);
xlabel('Time (day)')
ylabel('Concentrations (mg/L)')
legend ('Substrate')
 function Derivative = substrate (~,Ss,Y_H)
    global mu_H  Ks X_BH teta Ss_in
    Derivative = -((mu_H/Y_H)*(Ss/(Ks+Ss))*X_BH)+((1/teta)*(Ss_in-Ss)); %dSs/dt
Derivative=Derivative(:);
 end

Answer 2

[Star Strider]

Do not use global variables!

Pass the additional parameters as arguments to the function, and use an appropriate anonymous function call in ode45.

Try this:

mu_Hmax=0.15; %days^-1
T=22.6; %centigrade
X_BH=2295; %mg/l
teta=1.25; %day
Y_H=[0.6 0.7];
Ks=250; %mg/l
%initial condition is Ss_in=1127 mg/l
Ss_in=1127; %mg/l
mu_H=mu_Hmax*1.072^(T-20); %day^-1
tspan=[30 32 34 36 50 52 57 59 61 63 65 72 75 76 79 83 85 87 89 96 99 106 109 116 118 121 124 125 126 127 131 133 134 135 136 137 140];

for k = 1:numel(Y_H)
    [tv,Ssv(:,k)] = ode45(@(t,Ss)substrate(t, Ss, mu_H, Y_H(k), Ks, X_BH, teta, Ss_in),tspan,Ss_in);
end

figure
plot(tv,Ssv);
xlabel('Time (day)')
ylabel('Concentrations (mg/L)')
grid
legend (compose('Substrate: Y_H = %.1f',Y_H))

    function Derivative = substrate (t,Ss,u_H, Y_H, Ks, X_BH, teta, Ss_in)
        Derivative = -((mu_H/Y_H)*(Ss/(Ks+Ss))*X_BH)+((1/teta)*(Ss_in-Ss)); %dSs/dt
        Derivative=Derivative(:);
    end

EDIT — (8 Jan 2021 at 16:08)

Corrected typographical error.