# Bisection method using ode23

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Francesca Sbarbati on 21 Oct 2021
Answered: Francesca Sbarbati on 22 Oct 2021
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

Francesca Sbarbati on 22 Oct 2021
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-')

R2019a

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