The solution here divided into tow steps: from t0-tc and from tc-tf. then the total solution added into one (which is x as shown in the final row)
I'm solving using modefied euler method, and then finding Jacobian matrix (Fi_x). after running the code it gives me jacobian matrix 6x4. but it should be 6x6 because I have here n=6 and jacobian matrix should be in 6x6 dimension.
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kmax=(tc-t0)/h;
Xd1=[x0];
Tm1=[t0];
for k=1:kmax
t1=k*h;Tm1=[Tm1 t1];
xd=modeu(Fdfpek,t1,x0,h);
xp1=x0+eps*v1;
Fi2=modeu(Fdfpek,t1,xp1,h);
Fi1=xd;
Fix1=(1./eps)*(Fi2-Fi1);
%-----------------------
xp2=x0+eps*v2;
Fi2=modeu(Fdfpek,t1,xp2,h);
Fi1=xd;
% second column of Fi_x
Fix2=(1./eps)*(Fi2-Fi1);
Fi_x1=[Fix1 Fix2];
Fi_xM1(:,:,k)=Fi_x1;
%-----------------------
Xd1=[Xd1; xd'];
x0=xd';
end
x0c =Xd1(kmax,:);
Y=abs(Yaf); th=angle(Yaf);
nmax=(tf-tc)/h;
Xc1=[x0c];
Tm2=[tc];
for n=1:nmax
t2=n*h+tc;Tm2=[Tm2 t2];
xa=modeu(Fafpek,t2,x0c,h);
xp11=x0c+eps*v3;
Fi2=modeu(Fafpek,t2,xp11,h);
Fi1=xa;
Fix1=(1./eps)*(Fi2-Fi1);
%-----------------------
xp22=x0c+eps*v4;
Fi2=modeu(Fafpek,t2,xp22,h);
Fi1=xa;
% second column of Fi_x
Fix2=(1./eps)*(Fi2-Fi1);
Fi_x2=[Fix1 Fix2];
Fi_xM2(:,:,n)=Fi_x2;
%-----------------------
x1(n+1)=xa(1);
x2(n+1)=xa(2);
Xc1=[Xc1; xa'];
x0c=xa';
end
Fi_x=[Fi_xM1(:,:,k), Fi_xM2(:,:,n)];
.......................................................................
t =[Tm1'; Tm2']; x = [Xd1; Xc1];
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