solving pohlhausen equation,how I can write true function?

I write this function for solve pohlhausen equation.(T''+Pr/2 F T'=0 ) That F is output of blasius equation( 2F'''+FF''=0).but my code has error.how I can write true function?

function [Tetadot,fdot]=pohlhausen(eta,Teta,f);
 fdot=blasius(eta,f);
 Tetadot(1)=Teta(2);
 Tetadot(2)=-(0.7/2)*f(1)*Teta(2);
 Tetadot=Tetadot';
  function fdot=blasius(eta,f); 
    fdot(1)=f(2);
    fdot(2)=f(3);
    fdot(3)=-(1/2)*f(1)*f(3);
    fdot=fdot';
  end
end

[mahdi etminan]

I solve the blasius equation numerically.

clear all;
clc;
p1=0.01;
p2=1;
Err=0.00001;
i=1;
err=1;
while err>Err
    if i==1
       [eta, f]=ode45('blasius1',[0:0.2: 10],[0 0 p1]);
        m1=f(end,2);
        [eta,f]=ode45('blasius1',[0:0.2: 10],[0 0 p2]);
        m2=f(end,2);
    else
        p2=p1+(p2-p1)*(1-m1)/(m2-m1);
        [eta,f]=ode45('blasius1',[0:0.2: 10],[0 0 p2]);
         m2=f(end,2);
         err=abs(1-m2);
    end
    i=i+1;
end 

that the function of blasius is:

function fdot=blasius1(eta,f); 
fdot(1)=f(2);
fdot(2)=f(3);
fdot(3)=-(1/2)*f(1)*f(3);
fdot=fdot';

I do not know how replace F data in pohlhausen's function to earn Teta numerically.

n1=0.01;
n2=1;
Er=0.00001;
j=1;
er=1;

while er>Er
    if j==1
        [eta,Teta]=ode45('pohlhausen',[0:0.2: 10],[0 n1]);
        h1=Teta(end,1);
        [eta,Teta]=ode45('pohlhausen',[0:0.2: 10],[0 n2]);
        h2=Teta(end,1);
    else
        n2=n1+(n2-n1)*(1-h1)/(h2-h1);
        [eta,Teta]=ode45('pohlhausen',[0:0.2: 10],[0 n2]);
         h2=Teta(end,1);
         er=abs(1-h2);
    end
    j=j+1;
 

pohlhausen function that I write is:

function [Tetadot,fdot]=pohlhausen(eta,Teta,f);
 fdot=bla(eta,f);
 Tetadot(1)=Teta(2);
 Tetadot(2)=-(0.7/2)*f(1)*Teta(2);
 Tetadot=Tetadot';
  function fdot=bla(eta,f); 
    fdot(1)=f(2);
    fdot(2)=f(3);
    fdot(3)=-(1/2)*f(1)*f(3);
    fdot=fdot';
  end
end

end

[Torsten]

You'll have to solve both equations (Blasius and Pohlhausen) together, not one after the other.

Answer 1

[Star Strider]

If you have the Symbolic Math Toolbox, let it do the programming for you:

% % 2F'''+FF''=0
% % T''+Pr/2 F T'=0
syms F(t) Pr T(t) t Y 
Blasius = 2*diff(F,3)+F*diff(F,2) == 0;
Polhausen = diff(T,2) + Pr/2 * F * diff(T) == 0;
[VF,Sbs] = odeToVectorField(Blasius, Polhausen)             % Vector Field Representation & Substitutions
polhfcn = matlabFunction(VF, 'Vars',{t,Y,Pr})               % Anonymous Function
varcell = sym2cell(Sbs);                                    % Cell Array Of Substitutions
varstr = sprintfc('%s',[varcell{:}]);                       % Cell Array Of Substitution Strings (For ‘legend’ Or Other Uses), Can Also Use The ‘compose’ Function

producing:

polhfcn =  @(t,Y,Pr) [Y(2);Pr.*Y(2).*Y(3).*(-1.0./2.0);Y(4);Y(5);Y(3).*Y(5).*(-1.0./2.0)];

and other information.

You would define a value for ‘Pr’ in your workspace, then use the function (in ode45, for example, although I have no idea what solver is most appropriate here):

[t,y] = ode45(@(t,Y)polhfcn(t,Y,Pr), tspan, ics);

Check to be sure I entered the equations correctly. I believe I did, although it is always appropriate to check.