3rd order non-linear differential equation (shooting method)

Hi, I have to solve the following equation --- f*f'' + 2*f''' = 0 with the boundary conditions --- for eta = 0: f = 0, f' = 0 and for eta = infinity (let's say it's 20): f' = 1 and I have a problem with the shooting method. If my initial solutions for f, f' and f'' are not near the real solution for the before mentioned then I don't get the right graph. Does anybody know what to do? Thanks in advance!

My code:

beskonacno = 20;

etaint = [0:.01:0.2 0.2:.02:0.8 0.8:.01:1]*20;

solinit = bvpinit(linspace(0,beskonacno,50000),@dbinit);

options = bvpset('stats','on');

sol = bvp4c(@difjedn,@rubuvj,solinit,options);

eta = sol.x;

f = sol.y;

figure

plot(eta,f(1,:),'b',eta,f(2,:),'m',eta,f(3,:),'k');

axis([0 beskonacno -1000 1000]);

title(' Rješenje ')

xlabel('\eta')

ylabel('f , df/d\eta , d^2f/d\eta^2')

legend('f','df/d\eta','d^2f/d\eta^2')

fi = deval(sol,etaint);

Tablica = table(etaint',fi(1,:)',fi(2,:)',fi(3,:)','VariableNames',{'eta' 'f' 'df' 'd2f'})

a = fi(3,1)

function dfdeta = difjedn(eta,f)

dfdeta(1) = f(2);

dfdeta(2) = f(3);

dfdeta(3) = -(f(1)*f(3))/2;

end

function res = rubuvj(f0,fbes)

res = [f0(1);

f0(2);

fbes(2)-1;]

end

function yinit = dbinit(x)

yinit = [x^4;

4*x^3;

12*x^2;

];

end

Answer 1

[hashem]

let if you have many value for like f = -2s ,where s= -2.5,-2,-1.5,-1.-0.5,0 , what will be your code