Simultaneously numerically integrate multiple ODE's in MATLAB

I was trying to solve a system of muptiple ODEODE at the same time in Matlab but wasn't sure how should I solve for that.

So if I have

dy1/dx=sum of yi , i from 1 to j

dy2/dx=y1^2-y2*sum of yi, i from 1 to j

dy3/dx=y1*y2+y2^2- y3*sum of yi, i from 1 to j

and given initial condition that y1(0)=1 other yi=0 (i>1)

Could anyone have me with this please? Thank you!

[darova]

Show your attempts

[Rong Song]

K=10;

% Initial Conditio

for k=1:K

if k==1

yi(k)=1;

else

yi(k)=0;

end

end

b=0;

d=20;

% y include y1 y2 y3 y4...to yK

y=zeros(1,100);

for k=1:K

if k==1

y=e(k);

dydd{k}=@(y,t) -y(k)*sum(y);

else

y=e(k);

for j=1:k-1

b=b+y(j)*y(k-j);

end

dydd{k}=@(y,t) 1/(2*y(k))*b-y(k)*sum(y);

end

end

interval=linspace(0,d,100);

[t,y]=ode45(dydd,interval,yi);

Answer 1

[Pavel Osipov]

"I was trying to solve a system of multiple orders at the same time in Matlab but wasn't sure how should I solve for that". "is that right?"

Then imagine the left part as a system of equations of the 1st order and solve in Matlab in vector form. Good luck!

[Rong Song]

Do you mean treat the y1 y2... yi as a vector ? But ode45 doesn't allow me to integrate a vector.

Answer 2

[Pavel Osipov]