MATLAB: Ode45 code not running and need help imputing the boundary conditions

boundaryconditioncodeode45

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, …

Best Answer

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.
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