Solve "Index exceeds the number of array elements (1)", "Vectors must be the same length." errors

I'd like to solve those problems from under coding using A, B, and C relationships. If equation error can't be fixed, "B(i+1)=B(i)+((h.*q)/(k*T*E))*C(i)" can be used.

a = 0;
b = 1;
n = 110;
k = 8.61733*10^(-5); 
T = 300 ;
q = 1.60218*10^(-19);
E = 8.8542*10^(-12)
x= linspace(a,b,n);
h= x(2)-x(1);
A = zeros(size(x));
B = zeros(size(x));
for i = 0:n-1
    A(0)=3; 
    B(0)=1; 
    C(i)=2*x(i)+3;
    A(i+1)=A(i)-h.*B(i)-(0.5.*h.^2*q.*C(i))./(k*T*E);
    B(i+1)=B(i)+((h.*q)/(k*T*E))*0.5*(C(i)+C(i+1));%equation error
end
plot(transpose(x),A,'.')

[Tanmay Das]

Hi. Can you please try starting the index from 1 instead of 0 and go upto n in the for loop?

Answer 1

[Walter Roberson]

a = 0;
b = 1;
n = 110;
k = 8.61733*10^(-5); 
T = 300 ;
q = 1.60218*10^(-19);
E = 8.8542*10^(-12)
x= linspace(a,b,n);
h= x(2)-x(1);
A = zeros(size(x));
B = zeros(size(x));
A(0+1)=3; 
B(0+1)=1; 
for i = 0:n-1
    C(i+1)=2*x(i+1)+3;
    A(i+1+1)=A(i+1)-h.*B(i+1)-(0.5.*h.^2*q.*C(i+1))./(k*T*E);
    B(i+1+1)=B(i+1)+((h.*q)/(k*T*E))*0.5*(C(i+1)+C(i+1+1));
end
plot(transpose(x),A,'.')

[sookyung Kang]

I still have the same error message "Index exceeds the number of array elements (1).."

[Walter Roberson]

    C(i)=2*x(i)+3;

In that line you are writing into the "current" C -- you do not start out with a C, and you use and and you write to and and

    B(i+1+1)=B(i+1)+((h.*q)/(k*T*E))*0.5*(C(i+1)+C(i+1+1));

In that line you use the "current" C that you just wrote to ( on the first iteration), but you also use the "next" C, on the first pass, which has not been created yet.

In order to be able to use two generations of C values in that line, you will need to initialize the first C before the loop and write to the new C.

    a = 0;
b = 1;
n = 110;
k = 8.61733*10^(-5); 
T = 300 ;
q = 1.60218*10^(-19);
E = 8.8542*10^(-12)
x= linspace(a,b,n);
h= x(2)-x(1);
A = zeros(size(x));
B = zeros(size(x));
C = zeros(size(x));
A(0+1)=3; 
B(0+1)=1;
C(0+1) = something
for i = 0:n-1
    C(i+1+1)=2*x(i+1)+3;
    A(i+1+1)=A(i+1)-h.*B(i+1)-(0.5.*h.^2*q.*C(i+1))./(k*T*E);
    B(i+1+1)=B(i+1)+((h.*q)/(k*T*E))*0.5*(C(i+1)+C(i+1+1));
end
plot(transpose(x),A,'.')

[sookyung Kang]

Thanks!

Now I got a message that "Vectors must be the same length." to fix the plot. Do you have any idea about this plot? I tried to change simple plot as

plot(x,A,'.')

but I got the same wrong message..

[Walter Roberson]

Your looping structure is creating up to A(n-1+1+1) = A(n+1) but your x is length n. That is, your loop is creating n new elements beyond but your x is only expecting n elements total including

[sookyung Kang]

i = 0:n-2

it could make a graph but they don't show any change by C value as I changed the equation form..

[Walter Roberson]

Could you give an example of a changed equation form that is not resulting in a change to C ?

[sookyung Kang]

Like

C(i+1)=2*x(i+1)+1; C(i+1)=x(i+1)+3;

etc..

[Walter Roberson]

What are you initializing C(1) to ? (0.5.*h.^2*q)./(k*T*E) is about 3E-11 so unless C is pretty big, the value being subtracted in forming A(i+1+1) is not going to make much difference to A.

Furthermore, in comparing the two possibilities 2*x(i+1)+1 compared to x(i+1)+3, your first x is 0, and 2*0 is the same as 1*0, so your second C is going to be 1 in the first case or 3 in the second case, no matter what you initialized C(1) to, and as noted above, you need a C on the order of 1E10 to make much difference to A.

[sookyung Kang]

Actually I've tried to find out C equation by putting new formula: cos(x), constant not zero, cosh(x), x^2 etc..

And I realized E is 11.9.

[Walter Roberson]

So E is 11.9 instead of 8.8542*10^(-12)?

Do I understand correctly that you do not know the formula for C and are trying to figure out what it is? If that is the case then what final result do you need for A in order to know that you got the right C formula?

[sookyung Kang]

Yes. And no. I need to figure out that C equation by comparing theoretical equation as I didn't put this code.

[Walter Roberson]

Which theoretical equation are you comparing to, and which result from your program are you comparing it to?

How do you know when you have reached and adequate solution?

Answer 2

[Tanmay Das]

Hi,

I have the understanding that you are facing trouble in indexing of arrays. Unlike C++ or Python, indexing starts from 1 in MATLAB. So if you write A(0), then it will throw error. The following code may be useful for your understanding:

a = 0;
b = 1;
n = 110;
k = 8.61733*10^(-5); 
T = 300 ;
q = 1.60218*10^(-19);
E = 8.8542*10^(-12)
x= linspace(a,b,n);
h= x(2)-x(1);
A = zeros(size(x));
B = zeros(size(x));
A(1)=3; 
B(1)=1; 
C = 2*x + 3
for i = 1:n-1    
    A(i+1)=A(i)-h.*B(i)-(0.5.*h.^2*q.*C(i))./(k*T*E);
    B(i+1)=B(i)+((h.*q)/(k*T*E))*0.5*(C(i)+C(i+1));%equation error
end
plot(transpose(x),A,'.')

Also please note that similar operations on each element of array can be done at once in MATLAB and do not require to run a loop like in case of C.

C = 2*x + 3

Hope that helps!

[sookyung Kang]

Thanks for your reply.

But no it is not correct. It doesn't reflect C value as I could see same graph.

I've followed Walter Roberson's coding. Now I'm in the situation to fix the ploting graph as loop structure and x length are different.