Index exceeds the number of array elements

function [x, y1, y2, y3, y4 ] = FDEx4_1(N,kn,F)
clc
mm = 4;
N = 200;
h = 1/N;% mesh size
kn = 0.5;%Reynolds number
F = 0.23;

x = (0:h:1)'; % nodes
M = zeros(mm*(N+1),mm*(N+1));
b = zeros(mm*(N+1),1);

Done = 0;
Max_iter = 10;


y0 = zeros(mm*(N+1),1);
for i = 1:N+1
   y0(mm*(i-1)+1) = 0;
   y0(mm*(i-1)+2) = 0;
   y0(mm*(i-1)+3) = 0;
   y0(mm*(i-1)+4) = 0;
end

y1 = zeros(N+1,1);
y2 = zeros(N+1,1);
y3 = zeros(N+1,1);
y4 = zeros(N+1,1);
for i = 1:N+1
    y1(i) = x(mm*(i-1)+1);
    y2(i) = x(mm*(i-1)+2);
    y3(i) = x(mm*(i-1)+3);
    y4(i) = x(mm*(i-1)+4);
end

iter = 0;

while (~Done)
    for i = 1:N
        xip1 = 0.5*(x(i)+x(i+1));
        yip1 = 0.5*(y0(mm*(i-1)+1:mm*i)+y0(mm*i+1:mm*(i+1)));

        Aip1= [0,-1./kn, 0, 0;
            0, 0, -F./(yip1(3)).^2, 0;
            0, 0, 0, -4./(15*kn);
            0, (2*yip1(2))./(kn), 0, 0];
        Qip1 = [-(yip1(2))./kn; F./yip1(3); (4*yip1(4))./(15*kn); ((yip1(2)).^2)./kn];
        fip1 = Qip1-Aip1*yip1;
        M(mm*(i-1)+1:mm*i,mm*(i-1)+1:mm*i) = -(0.5*Aip1+eye(mm)/h);
        M(mm*(i-1)+1:mm*i,mm*i+1:mm*(i+1)) = (-0.5*Aip1+eye(mm)/h);
        b(mm*(i-1)+1:mm*i) = fip1;
    end 
    
    Ba = [sqrt(2./pi*y3(0)), 1, -(y1(0))*(1./sqrt(pi*2)*(y3(0).^1.5)), 0;
        0, 0, 0, 0;
        0, 0, (sqrt(2)*(1./(y3(0)).^1.5)*sqrt(pi))*(y3(0) + 1), 1;
        0, 0, 0, 0];
    Bb = [0, 0, 0, 0;
        -sqrt(2./(pi*y3(1))), 1, y1(1)*(1./(y3(0)).^1.5*sqrt(2*pi)), 0;
        0, 0, 0, 0;
        0, 0, -(sqrt(2)*(1./(y3(0)).^1.5)*sqrt(pi))*(y3(1) + 1), 1];
     
    M(mm*((N+1)-1)+1:mm*(N+1),mm*((N+1)-1)+1:mm*(N+1)) = Bb;
    M(mm*((N+1)-1)+1:mm*(N+1),1:mm) = Ba;
    alpha = [0; 0; 0; 0];
    b(mm*((N+1)-1)+1:mm*(N+1)) = alpha;
    
    x = M\b;
    
    error = max(abs(x-y0));% max |y_i-y_i^*|
    iter = iter+1;
    disp(['Error in step ',num2str(iter),' is : ',num2str(error)])
    y0 = x;

    Done = (iter>=Max_iter)||(error<0.000001);
    
    
end

It says

Index exceeds the number of array elements (201).

Error in FDEx4_1 (line 31)

y2(i) = x(mm*(i-1)+2);

How do i fix this?

[per isakson]

Write some comments, which explains what the loops are intended to achieve.

Answer 1

[VBBV]

%if true
  x = 0:h:1;% size has 201 elements

Define this according to function calculations e.g.

 x = 0:1/((N+1)*mm):1;% size of 805

[Naman Singh]

Ba = [sqrt(2./pi*y3(0)), 1, -(y1(0))*(1./sqrt(pi*2)*(y3(0).^1.5)), 0;

In this line it gives an error of

Array indices must be positive integers or logical values.

[VBBV]

Matlab does not use zero or decimal indexing for matrix definitions. Since y1 and y3 are matrices using 0 as index which is undefined in matlab, it produces error.

You can set it to y1(1) or y3(1) if you want to use only first element of those matrix

[VBBV]

in the same function you are also trying to calculate x vector using the matrix inversion operator \

[VBBV]

Also an end statement for the function is required