problem with Euler's explicit methode

clc
clear all

%%%%%%%%%%%%%Entering the variable%%%%%%%%%%%%%%%%%

Vn=1.52*(10^-5) ; %Volumen start punkt
Vch4=53/100 ;
Vco2=47/100 ;

%PV=nRT...... V/n=RT/P aber R,T und P are constant:
%V=n; n=C.Vn....C=V/Vn

%k3= 0.008;
%k4= 0.001;
%k6=0.5;
%k8 = 0.048;
%Cco2=X     Cch4=Y      Ch2=Z      Cco= M      Ch2o= L       Cc=N

%dY/dt= -0.5*Y*L;                                  
%dL/dt=  0.016*X*Z -0.001*M*L -0.5*Y *L;       
%dX/dt= -0.008*X*Z -0.048*N*X +0.001*M*L;   
%dM/dt= -0.001*M*L +0.5*Y*L + 0.096*N*X;       
%dZ/dt= -0.016*X*Z +0.001*M*L +1.5*Y*L;       
%dN/dt= 0.008*X*Z -0.048*N*X;                      


y0= Vch4/Vn;      %34.868,421052631578947368421052632        %m0 consentration in Startpunkt für Methan
X0= Vco2/Vn;      %30.921,052631578947368421052631579        %k0 consentration in Startpunkt für CO2


t0=0;
tend=100;
h=0.1;
L0=0;M0=0;Z0=0;N0=0;
X(1)=X0;Y(1)=y0;L(1)=L0;M(1)=M0;Z(1)=Z0;N(1)=N0;
k=(tend-t0)/h;


%%% solution
t(1)=t0;
func1=@(Y,L) -0.5*Y*L;                                   %dY/dt
func2=@(X,Z,M,Y,L) 0.016*X*Z -0.001*M*L -0.5*Y *L;        %dL/dt
func3=@(X,Z,M,L,N) -0.008*X*Z -0.048*N*X +0.001*M*L;    %dX/dt
func4=@(M,L,Y,N,X) -0.001*M*L +0.5*Y*L + 0.096*N*X;       %dM/dt
func5=@(X,Z,M,L,Y) -0.016*X*Z +0.001*M*L +1.5*Y*L;       %dZ/dt
func6=@(X,Z,N)0.008*X*Z -0.048*N*X;                       %dN/dt



%% Euler
for i=1:k-1
    
t(i+1)=i*h;
Y(i+1)=Y(i)+ h*func1(Y(i),L(i));
L(i+1)=L(i)+h*func2(X(i),Z(i),M(i),L(i),Y(i)); 
X(i+1)=X(i)+h*func3(X(i),Z(i),N(i),M(i),L(i)); 
M(i+1)=M(i)+h*func4(M(i),L(i),Y(i),N(i),X(i));
Z(i+1)=Z(i)+h*func5(X(i),Z(i),M(i),L(i),Y(i));
N(i+1)=N(i)+h*func6(X(i),Z(i),N(i)) ;



end


figure(1)
plot (t,Y)
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('CH4');
figure(2)        
plot(t,X)
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('CO2');
figure(3)                    
plot(t,L)
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('H2O');
figure(4)                  
plot(t,Z)
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('H2');
figure(5)                   
plot(t,M);
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('Co');
figure(6)                   
plot(t,N);
xlabel('Zeit in S');
ylabel('konzentration in mol/l')
title('C');

I would like to write a program for solving 6 equations with 6 variables throw Euler's explicit methode ,but all the Variable take just 0 value.

it is somthing for my University Homwork

Answer 1

[Alan Stevens]

Because you have initial values of zero for

L0=0;M0=0;Z0=0;N0=0;

and they multiply the terms on the right-hand side of your func equations, there is never anything to change the values of Y, L, X ... etc.

Also you need to make sure that you call the functions with the arguments in the same order as specified in the function definitions.

L(i+1)=L(i)+h*func2(X(i),Z(i),M(i),L(i),Y(i)); 
X(i+1)=X(i)+h*func3(X(i),Z(i),N(i),M(i),L(i)); 

should be

L(i+1)=L(i)+h*func2(X(i),Z(i),M(i),Y(i),L(i));  
X(i+1)=X(i)+h*func3(X(i),Z(i),M(i),L(i),N(i)); 

[Ibrahim Alfathi]

but this is the Idea from Euler explicit to give the Programm intitial value ( which is Elementary terms in m Programm with 0 value ) to find the solution throw : order

for i=1:n

.

.

.

end

what i should chang to make right?

[Alan Stevens]

You need to provide a non-zero initial value somewhere for at least one of L0, M0, Z0 or N0.