How to use one ode45 to solve another?

I have the following for my first ODE:

t0=0; tf=7;
y0=[0 0 0.332]'; 
[t,y]=ode45('ydot',[t0 tf],y0);

'ydot' is shown below:

function xdot = ydot(t,y) 
xdot = zeros(3,1); 
xdot(1) = y(2);
xdot(2) = y(3);
xdot(3) = -0.5*y(1)*y(3);
end

I now have a separate set of equations, where I need y from the initial solution.

function zdot = gdot(t,g)
zdot = zeros(2,1);
zdot(1) = g(2);
zdot(2) = -0.5*Pr*y(1)*g(2);
end

The second ode45 I need to solve is below.

t0=0; tf=7; Pr=0.6;
%y0=[0 0 0.332]'; 
%[t,y]=ode45('ydot',[t0 tf],y0);
g0=[0 0.332*Pr^(1/3)]';
[t,g]=ode45('gdot',[t0 tf],g0);

Any help is greatly appreciated.

Answer 1

[David Goodmanson]

Hi Carlos,

you can toss them all in together, with g(1) = y(4) and g(2) = y(5). That way y(1) is available in context.

t0=0; tf=7;
Pr = 0.6;
y0=[0 0 0.332 0 0.332*Pr^(1/3)]'; 
[t,y]=ode45(@ydotcalc,[t0 tf],y0);
fig(1)
plot(t,y);grid on

function ydot = ydotcalc(t,y) 
Pr = 0.6;
ydot = zeros(5,1); 
ydot(1) = y(2);
ydot(2) = y(3);
ydot(3) = -0.5*y(1)*y(3);
ydot(4) = y(5);
ydot(5) = -0.5*Pr*y(1)*y(5);
end

[Carlos Ojeda]

This worked perfect. Thanks so much, David!

Maybe you could help with the rest of the solution. I now wish to plot T(y) with the following info:

U_inf = 1; %Free stream velocity
T_s = 300; %Surface temperature Celsius
T_inf = 27; %Ambient temperature
v = 30E-6; %m^2/s
x = 0.5; %distance (m)
Re_x = U_inf*x/v; %Reynolds

T(y)=(((U_inf*v*x)^(1/2)*y(4))-T_s)/(T_inf-T_s);
figure(2)
plot(T,y);

But I'm getting an error. Can you help? Thanks!

[David Goodmanson]

Hi Carlos,

it looks like you might be intending

T = (((U_inf*v*x)^(1/2)*y(:,4))-T_s)/(T_inf-T_s);
figure(2)
plot(T,y(:,4));

but it's not so clear. What is the underlying equation here?