ODE45 error Inputs must be floats, namely single or double.

I am trying to make a plot of conversion using a differential equation. I have divided up my work into two m files. The first is this

function dy = HWFOOL(t,y)
T = 300+200*y(1);
Kc = 10*exp(-6000/1.987*(1/450-1/T));
k = .01*exp((10000/1.987)*(1/300-1/T));
Fao = 0.2;
Cao = 0.1;
ra = -k*(Cao^2)*((1-y(1))^2-y(1)*Cao/Kc);

dy = sym(zeros(1,1));
dy(1) = -ra/Fao;

This runs fine and returns

ans =

(exp(1844508686086227/109951162777600 - 5533526058258681/(1099511627776*(200*y + 300)))*((y - 1)^2 - (y*exp(6640231269910417/989560464998400 - 6640231269910417/(2199023255552*(200*y + 300))))/100))/2000

My second m file, which should plot the conversion is

timerange = [0 10];
initial = [0];

[T,Y]=ode45(@HWFOOL,timerange,initial);

plot(t,Y(:,1),'-');
title('Conversion')

This returns

>> plotODE
Error using odearguments (line 110)
Inputs must be floats, namely single or double.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in plotODE (line 5)
[T,Y]=ode45(@HWFOOL,timerange,initial);

I have tried using matlabFunction after googling my problem, shown below

HWFL = matlabFunction(HWFOOL(t,y))

timerange = [0 10];
initial = [0];

[T,Y]=ode45(HWFL,timerange,initial);

plot(t,Y(:,1),'-');
title('Conversion')

Which returns

>> plotODE

HWFL = 

      @(y)exp((-5.032712632108706e3)./(y.*2.0e2+3.0e2)+1.677570877369569e1).*((y-1.0).^2-y.*exp((-3.019627579265224e3)./(y.*2.0e2+3.0e2)+6.710283509478275).*(1.0./1.0e2)).*5.0e-4

Error using
symengine>@(y)exp((-5.032712632108706e3)./(y.*2.0e2+3.0e2)+1.677570877369569e1).*((y-1.0).^2-y.*exp((-3.019627579265224e3)./(y.*2.0e2+3.0e2)+6.710283509478275).*(1.0./1.0e2)).*5.0e-4
Too many input arguments.

Error in odearguments (line 87)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in plotODE (line 6)
[T,Y]=ode45(HWFL,timerange,initial);

I'm not sure how to get this to work, and I am relatively new to matlab. Any help would be greatly appreciated

Answer 1

[Walter Roberson]

The only way that HWFOOL could have returned the result you show,

(exp(1844508686086227/109951162777600 - 5533526058258681/(1099511627776*(200*y + 300)))*((y - 1)^2 - (y*exp(6640231269910417/989560464998400 - 6640231269910417/(2199023255552*(200*y + 300))))/100))/2000

is if you had passed a symbolic y to HWFOOL. However, that will not happen in practice as you timerange and initial are both numeric.

Your objective function must return specific numeric values, not a symbolic function. There should be no sym() in that code. A numeric t and numeric y will be passed in and it must create a numeric result.

You should not be using matlabFunction.

Just delete the sym() line from the HWFOOL that you posted at the top, and run with the other lines you show in plotODE

[DNye]

Awesome! Works perfectly, thank you so much. I changed my files to

function dy = HWFOOL(t,y)

T = 300+200*y(1);
Kc = 10*exp(-6000/1.987*(1/450-1/T));
k = .01*exp((10000/1.987)*(1/300-1/T));
Fao = 0.2;
Cao = 0.1;
ra = -k*(Cao^2)*((1-y(1))^2-y(1)*Cao/Kc);

dy(1) = -ra/Fao;

and

timerange = [0 10];
initial = [0];

[T,Y]=ode45(@HWFOOL,timerange,initial);

plot(T,Y,'-');
title('Conversion')

Then ran

>> HWFOOL(t,y)

ans =

(exp(1844508686086227/109951162777600 - 5533526058258681/(1099511627776*(200*y + 300)))*((y - 1)^2 - (y*exp(6640231269910417/989560464998400 - 6640231269910417/(2199023255552*(200*y + 300))))/100))/2000

and then

>> plotODE

And it works perfectly! Again thanks a million, especially for responding so quick.