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?

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Chen 2022-9-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1806680-euler-method-table-problem-why-my-fprintf-y-i-1-only-has-the-last-ans-my-y1-y-i-1-is-incorrect-a

评论： Chen 2022-9-16

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));

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Answer 1

Torsten 2022-9-16

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1806680-euler-method-table-problem-why-my-fprintf-y-i-1-only-has-the-last-ans-my-y1-y-i-1-is-incorrect-a#answer_1054805

编辑：Torsten 2022-9-16

在 MATLAB Online 中打开

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