Error plotting (Vector must be the same length)

clear all
clc
f=@(t,y) 4*y.^2;                          
F = @(t) 1/(4*(1-t));                  
a=0; b=0.95;
h=0.05;
n = (b-a)/h;

t = a:h:b;                                 
y = zeros(1,length(t));                      
y(1) = 0.25;                                 

%EULERS METHOD
for i = 2:n+1
    y(i) = y(i-1) + h*f(t(i-1),y(i-1));      
end
E=y;


fprintf(' Step number_i     time_t   Approximated solution  Exact solution    Relative Error\n')
for j = 1:n+1
    m=abs(E(j)-F(t(j)));
    n = abs(F(t(j)));
    kE = m/n;
    A(j) = F(t(j));
    fprintf('%5d %18f %15f %20f %15f \n',j,t(j),E(j),F(t(j)),kE)
    
end

plot(t,A,'.-k', t, E, 'o-r')
xlabel('x');
ylabel('y(t)'); 
grid on
title('Part(a) Plot');
legend('Exact solution','Eulers solution')

**It all works for the table, but I'm getting an error for plotting. It says the vectors should be in the same length, but I don't get the problem.

Please help me.

Thank you.

Answer 1

[Davide Masiello]

The vector A has 19 elements, whereas t and E have 20.

clear all
clc
f=@(t,y) 4*y.^2;                          
F = @(t) 1/(4*(1-t));                  
a=0; b=0.95;
h=0.05;
n = (b-a)/h;
        
t = a:h:b;                                 
y = zeros(1,length(t));                      
y(1) = 0.25;                                 
%EULERS METHOD
for i = 2:n+1
    y(i) = y(i-1) + h*f(t(i-1),y(i-1));      
end
E=y;
fprintf(' Step number_i     time_t   Approximated solution  Exact solution    Relative Error\n')

 Step number_i     time_t   Approximated solution  Exact solution    Relative Error

for j = 1:n+1
    m=abs(E(j)-F(t(j)));
    n = abs(F(t(j)));
    kE = m/n;
    A(j) = F(t(j));
    fprintf('%5d %18f %15f %20f %15f \n',j,t(j),E(j),F(t(j)),kE)
      
end

    1           0.000000        0.250000             0.250000        0.000000 
    2           0.050000        0.262500             0.263158        0.002500 
    3           0.100000        0.276281             0.277778        0.005387 
    4           0.150000        0.291548             0.294118        0.008738 
    5           0.200000        0.308548             0.312500        0.012648 
    6           0.250000        0.327588             0.333333        0.017237 
    7           0.300000        0.349051             0.357143        0.022658 
    8           0.350000        0.373418             0.384615        0.029114 
    9           0.400000        0.401306             0.416667        0.036866 
   10           0.450000        0.433515             0.454545        0.046266 
   11           0.500000        0.471102             0.500000        0.057795 
   12           0.550000        0.515490             0.555556        0.072118 
   13           0.600000        0.568636             0.625000        0.090183 
   14           0.650000        0.633305             0.714286        0.113373 
   15           0.700000        0.713520             0.833333        0.143776 
   16           0.750000        0.815343             1.000000        0.184657 
   17           0.800000        0.948299             1.250000        0.241361 
   18           0.850000        1.128154             1.666667        0.323108 
   19           0.900000        1.382700             2.500000        0.446920 

plot(t(1:end-1),A,'.-k', t(1:end-1), E(1:end-1), 'o-r')
xlabel('x');
ylabel('y(t)'); 
grid on
title('Part(a) Plot');
legend('Exact solution','Eulers solution')

[Seungryul Lee]

do you know how to use only first 19 elements of t and E, so that I can plot it?

How can I get rid of the last element of t and E

[Davide Masiello]

Yes

plot(t(1:end-1),A,'.-k', t(1:end-1), E(1:end-1), 'o-r')

I updated it in the answer too, so you can see the resulting plot.