I don't know how to solve problem of Euler method with round off error

Question

When $y(i+1)=y(i)+hf(t,y)$

if step size $h$ is small then this method is expected to occur round off error

thus we transhape this Euler form to $u(i+1)=u(i)+hf(t(i),u(i))+o(i+1)$

which $o(i)$ is round off error of each $u(i)$

then if we encounter the problem with absolute error of $|y(i)-u(i)|$ how we resolve this problem if round off error is infinite decimal point?

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Jul 22 '19 at 10:03
What do you mean with the second formula? Is that the definition of the truncation error? What is infinite in your last sentence? Do you mean exact arithmetic, that is, no restriction on the number of decimal or binary digits? — Lutz Lehmann, Jul 22 '19 at 10:39
not truncation error. it is round off error each euler fomula — seyunkim, Jul 22 '19 at 10:45
Read Euler's Method Global Error: How to calculate $C_1$ if $error=C_1h$, global error in Euler's method and linked posts here and also your recommended text book on numerical methods and then please refine your question. — Lutz Lehmann, Jul 22 '19 at 10:46
example 0.213465465898944.............................. infinite — seyunkim, Jul 22 '19 at 10:47
You mean the floating point error? Like explored in the example here: How to calculate the errors of single and double precision, or probably better the difference between the single and double precision result, as long as the floating point error in the double results does not dominate? — Lutz Lehmann, Jul 22 '19 at 10:50

0 Answers0