Timeline for What is the maximum attainable accuracy with a given set of $\alpha,\beta$?
Current License: CC BY-SA 4.0
11 events
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| Mar 24, 2021 at 14:26 | comment | added | Mithridates the Great | @k.dkhk Well, a rough explanation is that the accuracy of your solution is in the order of $h^{4}$ and the error that you are getting due to truncating terms of higher orders is in the order of $h^{5}$. In another word, $h^{4}$ is a really rough estimation of your accuracy and $h^{5}$ is a rough estimation of your error getting out of this stencil. | |
| Mar 24, 2021 at 14:22 | comment | added | k.dkhk | @AloneProgrammer ok thanks. My theoritical knowledge is very poor so excuse for asking stupid. What is the difference between between those orders? (order of accuracy vs order of error). thanks. | |
| Mar 24, 2021 at 13:34 | history | edited | Mithridates the Great | CC BY-SA 4.0 |
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| Mar 24, 2021 at 13:33 | comment | added | Mithridates the Great | @k.dkhk I think you are right it is 4 order accurate but the error is in the order of 5. | |
| Mar 24, 2021 at 13:31 | comment | added | k.dkhk | @AloneProgrammer I have implemented the method. It seems like it is order 4. Are certain that this is order 5? | |
| Mar 23, 2021 at 21:58 | comment | added | k.dkhk | @AloneProgrammer I understand the exact arguement for saying the order is 5? I know that our Taylors have error term of $O(h^5)$ but what is the reason that we can conclude that final stencils are fifth order accurate? | |
| May 2, 2020 at 16:36 | vote | accept | econmajorr | ||
| Mar 27, 2020 at 13:44 | comment | added | Mithridates the Great |
@econmajorr what do you mean using scipy? for any given $\alpha$ and $\beta$ the procedure is the same as here but you need to solve $\alpha + \beta + 1$ linear equations. So, if you are asking to solve this linear equations numerically by using scipy.linalg, the answer is: It might be possible, but you need to try it to know for sure.
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| Mar 26, 2020 at 8:13 | comment | added | econmajorr |
thank you for this very thorough answer! Simple question: Can I use scipy package to actualy give me the optimal coefficients for any set of $\alpha, \beta$?
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| Mar 25, 2020 at 5:01 | history | edited | Mithridates the Great | CC BY-SA 4.0 |
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| Mar 25, 2020 at 4:03 | history | answered | Mithridates the Great | CC BY-SA 4.0 |