Bound on global error of 2nd order Runge-Kutta

Asked Dec 14 '19 at 05:18

Active Jul 04 '20 at 14:14

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I am trying to find a second order Runge Kutta global error bound defined as $$|Y_j-y_j|\leq L$$ where $Y_j$ is a true value and $y_j $ is approximation of the function at that point. Does anyone have any good references where I could read about this

edited Jul 04 '20 at 14:14

Rodrigo de Azevedo

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asked Dec 14 '19 at 05:18

Don

What second order RK method? There are several, one could say infinitely many. – Lutz Lehmann Dec 14 '19 at 11:04
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In the main idea, the proof https://math.stackexchange.com/a/2365882/115115 applies, only that the $e_i$ have size $O(h^3)$, the constant depending on the truncation error, giving a global error $O(h^2)$. – Lutz Lehmann Dec 14 '19 at 11:46

Bound on global error of 2nd order Runge-Kutta

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