Why ODE15s does not work like an Euler's method with fixed point?
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When i run this code for Euler´s method, it runs Ok, but when i try to use ODE15s it shows a wrong answer. It is ODE15s well defined?. I'll appreciate your help.
function []=cr_NRTL(X0,x1,x2,l,L1)
global X1 X2 Xea estado
x1inicial=x1;
x2inicial=x2;
sol_daes=2; %1 Euler, 2 ODE
tspan=[0 l];
opts=odeset('NormControl','on','AbsTol',1e-10,'RelTol',1e-5);
for k=1:2
x1=x1inicial;
x2=x2inicial;
for i=1:L1
X1 = x1; X2 = x2;
%Para solucionar la envolvente
options = optimset('Display','off');
lb=[0,0,0,0,0,0,0,0,300];
ub=[1,1,1,1,1,1,1,1,400];
Xea=lsqnonlin(@funcion,X0,lb,ub,options);
X0=Xea;
for j=1:9
xea(i,j)=Xea(j);
end
%Para evaluar las residuales del ELV fuera de la envolvente
if k==1 && (Xea(7)>0.9999 || Xea(8)>0.9999)
if Xea(7)>1 || Xea(8)>1
Xea
end
cr_NRTL2(x1,x2,l);
break
else
xglobala=[x1; x2];
%Para solucionar las residuales del ELLV
switch sol_daes
case 1 %Euler
switch k
case 1
tao=0.02;
dxdt=cambioELLV(xglobala);
xsa=[xglobala(1)+dxdt(1)*tao;
xglobala(2)+dxdt(2)*tao];
case 2
tao=0.1;
dxdt=cambioELLV(xglobala);
xsa=[xglobala(1)-dxdt(1)*tao;
xglobala(2)-dxdt(2)*tao];
end
case 2 %ODE
switch k
case 1
[~,dxdt]=ode15s(@cambioELLV,tspan,xglobala,opts);
case 2
[~,dxdt]=ode15s(@cambioELLV,-tspan,xglobala,opts);
end
xsa=dxdt;
end
x1=xsa(1);
x2=xsa(2);
% if k==2
for j=1:2
xsalida(i,j)=xglobala(j);
% end
end
end
% end
% if k ==2
xe = xea;
% end
end
toc
% Grafica
hold on
if estado==1
plot(xe(:,1),xe(:,2),'r')
end
plot(xsalida(:,1),xsalida(:,2),'b');
end
end
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