# How to convert from euler´s method to ODE45?

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Cesar García el 20 de Dic. de 2015
i want to use ODE45 based in the next code.
% Parameters
um=0.54;
Km=0.03;
k1=0.4;
k2=1.24;
Csx=0.095;
Csp=0.15;
Cnx=0.20;
Rcsx=0.022;
Rcnx=0.26;
%Initial Conditions
X(1)=1.16;
S(1)=20.05;
N(1)=2.00;
P(1)=1.01;
V(1)=3;
Sin=60;
Nin=0;
%Specific growth rate, we need to be care here, because u is not a function of time and it looks like a DAE.
u(1)=um*((N(1)/S(1))/((N(1)/S(1))+Km));
%simulation time and step for euler tsim=25;
t(1)=0;
dt=0.00001;
i=1;
while t(i)<tsim
if t(i)>4.9 && t(i)<5.001
F1=0.8;
F2=0;
else
F1=0;
F2=0;
end
V(i+1)=V(i)+(F1+F2)*dt;
X(i+1)=X(i)+(u(i)*X(i))*dt-((F1+F2)/V(i))*X(i)*dt;
S(i+1)=S(i)-(Csx*u(i)*X(i)+Rcsx*X(i))*dt-(Csp*(k1*u(i)*X(i)+k2*X(i)))*dt+(F1/V(i))*Sin*dt-((F1+F2)/V(i))*S(i)*dt;
P(i+1)=P(i)+((k1*u(i)*X(i))+(k2*X(i)))*dt-((F1+F2)/V(i))*P(i)*dt;
N(i+1)=N(i)-((Cnx*u(i)*X(i))+(Rcnx*X(i)))*dt+(F2/V(i))*Nin*dt-((F1+F2)/V(i))*N(i)*dt;
if N(i+1)<0
N(i+1)=0;
end
u(i+1)=um*((N(i+1)/S(i+1))/((N(i+1)/S(i+1))+Km));
t(i+1)=t(i)+dt;
i=i+1;
end
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