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No, that's not me in the pic, that's Mr. Dave Brubeck. Yes, I like jazz.


Jul
2
awarded  Curious
Jun
4
accepted Truncation error of an integration method
Jun
4
comment Truncation error of an integration method
I edited the number of steps (which was $O(h^{−1})$ before) and accepted the answer. If my edit is correct, I believe it is appropriate to accept this answer
Jun
4
suggested suggested edit on Truncation error of an integration method
Jun
3
accepted Butcher's Tableau and Runge-Kutta 4
Jun
3
comment Butcher's Tableau and Runge-Kutta 4
Could you gather these comments into one answer please? I think they already provide a lot of information necessary to answer the post ;)
Jun
3
comment Butcher's Tableau and Runge-Kutta 4
Ok, those notes are really cool. Thanks!
Jun
3
awarded  Commentator
Jun
3
comment Butcher's Tableau and Runge-Kutta 4
I am guessing that I should look into the work of Butcher if I want to understand them huh?
Jun
3
asked Butcher's Tableau and Runge-Kutta 4
May
31
asked Truncation error of an integration method
May
30
accepted Runge-Kutta and Step doubling
May
27
revised Runge-Kutta and Step doubling
deleted 224 characters in body
May
27
revised Runge-Kutta and Step doubling
added 224 characters in body
May
27
comment Runge-Kutta and Step doubling
do you have any idea of the answer to question #5, which I included only now? Thanks
May
27
revised Runge-Kutta and Step doubling
added 58 characters in body
May
24
comment Runge-Kutta and Step doubling
Maybe I didn't express the question correctly. The second part is about the estimate of the truncation error and how we can use it to adapt the step size of the integration. In the book that I am reading - where I took the information from - they refer that those two equations are used to improve the numerical estimate of $y(x+2h)$, which we get after ignoring the terms $h^{6}$ and higher and then solve those two equations. From my guess, maybe Taylor expansion indicates that $\phi$ has those coefficients that add to $\frac{1}{15}$. Does it make any sense?
May
24
comment Runge-Kutta and Step doubling
Very cool! Thank you so much! This was truly helpful
May
24
comment Runge-Kutta and Step doubling
I have been studying Runge-Kutta (and other methods) from a book, but maybe I should do as you suggested and look into wikipedia. Indeed, I think @arkamis' answer states the same thing that you said in the first part of your answer. In the second part, you refer that I am missing an $h^{5}$, though I don't see where. Thanks for the very nice (and simple in a good way) explanation for the rationale behind everything!
May
24
asked Runge-Kutta and Step doubling