ode45 code not running and need help imputing my boundary conditions

here is my matlab function code and the error i keep getting when running it also i would like to know how and where i can put my boundary condition in this code

function ydot = kubieode(t, y )

%define variables making it more legible

% Numerical Integration of Differential Equation

% Numerical Integration of a 3rd order ODE using ODE45 solver embedded in

% MATLAB.

%Pr is the Prantl number of the concerned fluid respectively.

%Le: Lewis number

%Nb: Brownian motion parameter

%Nt: Thermophoresis parameter

Msq = 0.5;

Nt = 0.1;

Nb = 0.1;

Pr = 0.2;

Le = 1.0;

ydot = zeros(7, 1); % Pre-allocate

ydot(1) = y(2); % f '

ydot(2) = y(3); % f ''

ydot(3) = -y(1) * y(3) + Msq * y(2); % f''' = -y(1)*y(3) + 0.5*y(2 )

ydot(4) = y(5); % theta '

ydot(5) = -Pr * (Nb * y(7) * y(5) + Nt * y(5) * y(5)); % theta ''

ydot(6) = y(7); % psi '

ydot(7) = - (Nt/Nb) * ydot(5) - (Le/Nb) * y(1); % psi ''

end

HERER IS THE COMMAND WINDOW AND RESULT/ERROR

y0(1) = 0 % f

y0(2) = 0 % f'

y0(3) = 0 % f''

y0(4) = 0 % theta

y0(5) = 0 % theta'

y0(6) = 0 % psi

y0(7) = 0 % psi'

[t y] = ode45(@kubieode,[0,20],y0);

[t,y]; %to print

plot(t,y(:,1));

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

y0 =

0 0 0 0 0 0 0

Msq =

0.5000

Nt =

0.1000

Nb =

0.1000

pr =

0.2000

le =

1

??? Undefined function or variable 'y0'.

Error in ==> kubieode at 30

[t,y] = ode45('kubieode',[0,20] ,y0);

Error in ==> odearguments at 110

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

Error in ==> ode45 at 173

[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

[Torsten]

If you start with y0=0, y will be 0 for all times.

[Daniel Kubiat]

so what do i start with? and how do i impute my boundary conditions to this code

[Torsten]

See the code below on how to input your boundary conditions.

It's up to you to know which boundary conditions to take.

Answer 1

[Torsten]

function main
 y0=zeros(7,1);
 y0(1) = 0; % f
 y0(2) = 0; % f'
 y0(3) = 0; % f''
 y0(4) = 0; % theta
 y0(5) = 0; % theta'
 y0(6) = 0; % psi
 y0(7) = 0; % psi'
 [t y] = ode45(@kubieode,[0,20],y0);
 plot(t,y(:,1));
end

function ydot = kubieode(t, y ) 
 %define variables making it more legible
 % Numerical Integration of Differential Equation
 % Numerical Integration of a 3rd order ODE using ODE45 solver embedded in
 % MATLAB.
 %Pr is the  Prantl number of the concerned fluid respectively.
 %Le:  Lewis number 
 %Nb:  Brownian motion parameter
 %Nt:  Thermophoresis parameter 

 Msq = 0.5;
 Nt = 0.1;
 Nb = 0.1;
 Pr = 0.2;
 Le = 1.0;

 ydot = zeros(7, 1); % Pre-allocate 
 ydot(1) = y(2); % f ' 
 ydot(2) = y(3); % f '' 
 ydot(3) = -y(1) * y(3) + Msq * y(2); % f''' = -y(1)*y(3) + 0.5*y(2 ) 
 ydot(4) = y(5); % theta ' 
 ydot(5) = -Pr * (Nb * y(7) * y(5) + Nt * y(5) * y(5)); % theta '' 
 ydot(6) = y(7); % psi ' 
 ydot(7) = - (Nt/Nb) * ydot(5) - (Le/Nb) * y(1); % psi '' 

end

Put the code from above in a file, name it main.m, load it into MATLAB and run it.