Index exceeds the number of array elements (11)

I need help please. I am trying write a program with the following steps:

(i) to obtain x(i) and y(i), i=1,2,...,m

(ii) to create a data matrix with the following elements:

row 1: [x(i) y(i) x(i)^2 x(i)*y(i) x(i)^2*y(i) ...]

row 2: [x(i+1) y(i+1) x(i+1)^2 x(i+1)*y(i+1) x(i+1)^2*y(i+1)...]

row 3: [x(i+2) y(i+2) x(i+2)^2 x(i+2)*y(i+2) x(i+2)^2*y(i+2)...]

row 4: [x(i+3) y(i+3) x(i+3)^2 x(i+3)*y(i+3) x(i+3)^2*y(i+3)...]

row 5: ....

and so on.

Row 1 and row 2 has no problem. However, when I enter row 3, I get the following error: "Index exceeds the number of array elements (11)". Can someone help me how to fix this error? Appreciation in anticipation.

Here is what I have done:

clear

h = 0.01; % time step

x(1)=1;

y(1)=1;

m=10; h = 0.01;

dxdt = @(x,y) y;

dydt = @(x,y) x-x^3;

for i=1:1:m

x(i+1) = x(i) + h*dxdt(x(i), y(i));

y(i+1) = y(i) + h*dydt(x(i), y(i));

end

% Data Matrices X

X = [x(i) y(i) x(i)^2 x(i)*y(i) x(i)^2*y(i) x(i)*y(i)^2 y(i)^2 y(i)^3 y(i)*x(i)^3 x(i)*y(i)^3 y(i)^3 x(i)^4 y(i)*x(i)^4 y(i)^4;

x(i+1) y(i+1) x(i+1)^2 x(i+1)*y(i+1) y(i+1)*x(i+1)^2 x(i+1)*y(i+1)^2 y(i+1)^3 y(i+1)*x(i+1)^3 x(i+1)*y(i+1)^3 y(i+1)^3 x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)^4;

x(i+2) y(i+2) x(i+2)^2 x(i+2)*y(i+2) y(i+2)*x(i+2)^2 x(i+2)*y(i+2)^2 y(i+2)^3 y(i+2)*x(i+2)^3 x(i+2)*y(i+2)^3 y(i+2)^3 x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)^4];

[KSSV]

As you are using i+1,i+2, i+3....when you reach i = length(x)..the array will try to access i+1 and you will get this error.

[Editor]

@KSSV Thank you for your response. However, upon using 'm=length(x)', I get a zero matrix. I do not know what else I can do.

[KSSV]

Share your complete code.

[Editor]

@KSSV, Here is my code after making the change you suggested:

clear

h = 0.01; % time step
x(1)=1;
y(1)=1;
h = 0.01;
dxdt = @(x,y) y;
dydt = @(x,y) x-x^3;
m = length(x)-3;
for i=1:1:m
    x(i+1) = x(i) + h*dxdt(x(i), y(i));
    y(i+1) = y(i) + h*dydt(x(i), y(i));
end
% Data Matrices X
X = [x(i) y(i) x(i)^2 x(i)*y(i) x(i)^2*y(i) x(i)*y(i)^2 y(i)^2 y(i)^3 y(i)*x(i)^3 x(i)*y(i)^3 y(i)^3 x(i)^4 y(i)*x(i)^4 y(i)^4;
     x(i+1) y(i+1) x(i+1)^2 x(i+1)*y(i+1) y(i+1)*x(i+1)^2 x(i+1)*y(i+1)^2 y(i+1)^3 y(i+1)*x(i+1)^3 x(i+1)*y(i+1)^3 y(i+1)^3 x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)^4;
     x(i+2) y(i+2) x(i+2)^2 x(i+2)*y(i+2) y(i+2)*x(i+2)^2 x(i+2)*y(i+2)^2 y(i+2)^3 y(i+2)*x(i+2)^3 x(i+2)*y(i+2)^3 y(i+2)^3 x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)^4];

[Editor]

I still encounter an error. I need your help please.

Answer 1

[KSSV]

h = 0.01; % time step

dxdt = @(x,y) y;
dydt = @(x,y) x-x^3;
m = 100 ;
x = zeros(m,1) ;
y = zeros(m,1) ; 

x(1)=1;
y(1)=1;

for i=1:1:m-1
    x(i+1) = x(i) + h*dxdt(x(i), y(i));
    y(i+1) = y(i) + h*dydt(x(i), y(i));
end

% Data Matrices X

 X = [x y x.^2 x.*y x.^2.*y x.*y.^2 y.^2 y.^3 y.*x.^3 x.*y.^3 y.^3 x.^4 y.*x.^4 y.^4];

    

[Editor]

Thank you very much @KSSV . The code resolves the error. However, from row 3 downwards, I get rows of zeros. What could be the issue? Is there a way in which I can do to resolve this?

[KSSV]

I am not getting any zeros. Can you be more clear?

[Editor]

I mean when I increase the number of rows as follows:

h = 0.01; % time step

dxdt = @(x,y) y;

dydt = @(x,y) x-x.^3;

m = 100 ;

x = zeros(1,m);

y = zeros(1,m);

x(1)=1;

y(1)=1;

for i=1:m-5

x(i+1) = x(i) + h*dxdt(x(i), y(i));

y(i+1) = y(i) + h*dydt(x(i), y(i));

end

X = [x(i) y(i) x(i)^2 x(i)*y(i) x(i)^2*y(i) x(i)*y(i)^2 y(i)^2 y(i)^3 y(i)*x(i)^3 x(i)*y(i)^3 y(i)^3 x(i)^4 y(i)*x(i)^4 y(i)^4;

x(i+1) y(i+1) x(i+1)^2 x(i+1)*y(i+1) y(i+1)*x(i+1)^2 x(i+1)*y(i+1)^2 y(i+1)^3 y(i+1)*x(i+1)^3 x(i+1)*y(i+1)^3 y(i+1)^3 x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)*x(i+1)^4 y(i+1)^4;

x(i+2) y(i+2) x(i+2)^2 x(i+2)*y(i+2) y(i+2)*x(i+2)^2 x(i+2)*y(i+2)^2 y(i+2)^3 y(i+2)*x(i+2)^3 x(i+2)*y(i+2)^3 y(i+2)^3 x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)*x(i+2)^4 y(i+2)^4;

x(i+3) y(i+3) x(i+3)^2 x(i+3)*y(i+3) y(i+3)*x(i+3)^2 x(i+3)*y(i+3)^2 y(i+3)^3 y(i+3)*x(i+3)^3 x(i+3)*y(i+3)^3 y(i+3)^3 x(i+3)^4 y(i+3)*x(i+3)^4 y(i+3)*x(i+3)^4 y(i+3)^4;

x(i+4) y(i+4) x(i+4)^2 x(i+4)*y(i+4) y(i+4)*x(i+4)^2 x(i+4)*y(i+4)^2 y(i+4)^3 y(i+4)*x(i+4)^3 x(i+4)*y(i+4)^3 y(i+4)^3 x(i+4)^4 y(i+4)*x(i+4)^4 y(i+4)*x(i+4)^4 y(i+4)^4;

x(i+5) y(i+5) x(i+5)^2 x(i+5)*y(i+5) y(i+5)*x(i+5)^2 x(i+5)*y(i+5)^2 y(i+5)^3 y(i+5)*x(i+5)^3 x(i+5)*y(i+5)^3 y(i+5)^3 x(i+5)^4 y(i+5)*x(i+5)^4 y(i+5)*x(i+5)^4 y(i+5)^4]

I get the followwing:

X =

Columns 1 through 12

1.5475 -0.2579 2.3949 -0.3991 -0.6176 0.1029 0.0665 -0.0171 -0.9557 -0.0265 -0.0171 5.7355

1.5450 -0.2795 2.3869 -0.4318 -0.6671 0.1207 -0.0218 -1.0306 -0.0337 -0.0218 5.6974 -1.5922

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

Columns 13 through 14

-1.4790 0.0044

-1.5922 0.0061

0 0

0 0

0 0

0 0

[KSSV]

For those last values, you have not fixed the value of i, so it will take i = m-5..what exactly you want to do with the last lines?

[Editor]

I want to form an mxn matrix (which is X in this case) with n-rows using [x(i) y(i) x(i)^2 x(i)*y(i) x(i)^2*y(i) ...] as my data. Rows should start as follows:

row 1: x(i)

row 2: x(i+1)

row 3: x(i+2)

.....

row n: x(i+n)

I need i to start, say, at index 1 or 3

[Editor]

I know your schedule is tight but I will appreciate if you can assist me fixing this problem above. Thank you in anticipation

[KSSV]

Hey..I have edited the answer.....please check..

[Editor]

@KSSV it works perfectly! Thank you so much for your time. You've been so helpful and patient