Euler method table problem.Why my fprintf(y(i+1)) only has the last ans, my y1-y(i+1) is incorrect and how to let the table be tidy?

h=0.2;

x=0:h:1;

y=zeros(size(x));

y(1)=0;

n=numel(y);

y1=exp(x)-x-1;

fprintf('xn \t yn\t y(xn)\t error\n ');

for i=1:n-1

f = x(i)+y(i);

y(i+1) = y(i) + h * f;

end

fprintf('%f\t %f\t %f\t %f\n',x,y(i+1),y1,y1-y(i+1));

Answer 1

[Torsten]

h=0.002;
x=0:h:1;
y=zeros(size(x));
y(1)=0;
n=numel(y);
y1=exp(x)-x-1;
for i=1:n-1
    f = x(i)+y(i);
    y(i+1) = y(i) + h * f;
end
hold on
plot(x,y)
plot(x,y1)
hold off

Xn = x.';
Yn = y.';
Exact_Yn = y1.';
Error = abs(y.'-y1.');
T = table(Xn,Yn,Exact_Yn,Error)

T = 501×4 table
     Xn          Yn         Exact_Yn       Error   
    _____    __________    __________    __________

        0             0             0             0
    0.002             0    2.0013e-06    2.0013e-06
    0.004         4e-06    8.0107e-06    4.0107e-06
    0.006    1.2008e-05    1.8036e-05    6.0281e-06
    0.008    2.4032e-05    3.2086e-05    8.0535e-06
     0.01     4.008e-05    5.0167e-05    1.0087e-05
    0.012     6.016e-05    7.2289e-05    1.2129e-05
    0.014    8.4281e-05    9.8459e-05    1.4178e-05
    0.016    0.00011245    0.00012869    1.6236e-05
    0.018    0.00014467    0.00016298    1.8302e-05
     0.02    0.00018096    0.00020134    2.0377e-05
    0.022    0.00022133    0.00024378    2.2459e-05
    0.024    0.00026577    0.00029032     2.455e-05
    0.026     0.0003143    0.00034095    2.6649e-05
    0.028    0.00036693    0.00039568    2.8756e-05
     0.03    0.00042366    0.00045453    3.0872e-05

[Chen]

thank you!

Do you know how to let Xn Yn Y(Xn) Error on top of the deta?

[Torsten]

See above.

[Chen]

Thank you for your help!!