Bisection method using ode23

Hi! I must use the shooting method by using bisection method to find root of f(s).

When I put "[x,u]= nlshoot1(10,0,2,0.01);" in the command window to verify the efficience, I get some errors.

I've tried as follows:

function [x,u]= nlshoot1(N,a0,b0,tol)

epi=exp(pi);
ak=a0;
bk=b0;
sk=(ak+bk)/2;
h=pi/N;
x=0:h:pi; 

[xx,uv]= ode23(@fun,x,[ak 2*ak]); 
fak=uv(N+1,1)-epi; 

[xx,uv]= ode23(@fun,x,[bk 2*bk]); 
fbk=uv(N+1,1)-epi;      

[xx,uv]= ode23(@fun,x,[sk 2*sk]);
fk=uv(N+1,1)-epi; 

afk=abs(fk);

while  afk>=tol 
    
    if fak*fbk<0
    sk=(ak+bk)/2;
    
    [xx,uv]= ode23(@fun,x,[sk 2*sk]);
    fk=uv(N+1,1)-epi; 
    
    if fk==0
        %I have a root

    else
       if fk*fak<0
       bk=sk;
     
       else  
        ak=sk; 
        [xx,uv]= ode23(@fun,x,[sk 2*sk]);
        fk=uv(N+1,1)-epi; 
       end
    end
    else 
   end
     
afk=abs(fk);
 
end 
u=uv(:,1); 
end


function uvp= fun(x,uv)
uvp=[uv(2); (exp(-x)/2*(uv(2)^2+uv(1)^2))-(exp(-x)/2+cos(x)+2*sin(x))];
%u is the first component and v is the second component
end

Answer 1

[Francesca Sbarbati]

I solve this problem choosing a good value of a0 and b0.

I write in the Command window the following commands:

[x,u]= nlshoot1(10,0,1.01,0.001);
y=exp(x)+sin(x); %to compare the solution
plot(x,u,'r*',x,y,'k-')