Implicit Trapezoidal Rule

Asked Sep 26 '21 at 06:58

Active Sep 26 '21 at 07:32

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Integrate $y' = \sin(y)$, $y_0 = 2$; using $h = 0.1$ with the implicit Trapezoidal rule, to compute $y_1$ within approximate relative error $e<10^{-5}$.

I first tried to apply the Trapezoidal rule which then resulted in an implicit equation. To solve that, then I tried going by Newton's method and it is still not working well for me. So, I assumed an initial approximation $y_n^{(0)}$ and iterated the whole equation to make it converge to $y_n$, but again I am getting stuck somewhere. Any help would be appreciated.

edited Sep 26 '21 at 07:32

asked Sep 26 '21 at 06:58

Damini

What is your definition of $y_1$? Is it $y(x_0+h)$ or $y(x_0+1)$ or something else completely different? – user10354138 Sep 26 '21 at 07:34
It is $y(x_0 + h)$ only. – Damini Sep 26 '21 at 09:40
Please, if you could document how you applied the Newton method, what function, what derivative or its approximation. – Lutz Lehmann Sep 26 '21 at 10:28

Implicit Trapezoidal Rule

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