Timeline for Numerical solution of Fredholm Equation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2021 at 0:56 | comment | added | Aksakal | @MariuszIwaniuk 0.657412. you can get it with high precision using my approach mathematica.stackexchange.com/a/244172/79287 | |
| Apr 5, 2021 at 15:50 | comment | added | Mariusz Iwaniuk |
Looks like at x=0 value is not 2/3.Try: N[Expand[DSolveValue[\[Phi][x] == 1 - 1/Pi* Integrate[\[Phi][ t]*(Series[1/(1 + (x - t)^2), {x, 0, 4}] // Normal) // Simplify // Expand, {t, -1, 1}], \[Phi][x], x]], 20]
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| Apr 5, 2021 at 12:07 | comment | added | Alex Trounev |
@MariuszIwaniuk Ah, I see, that your method also gives 0.657412 for n=10. May be true value is not 2/3?
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| Apr 5, 2021 at 11:30 | comment | added | Mariusz Iwaniuk |
I tried with nN = 36 and give me: 0.6574115... ?
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| Apr 5, 2021 at 10:57 | comment | added | Alex Trounev |
@MariuszIwaniuk Actually 2/3=0.66666..., and colocation method gives solution with some error of $h^2$. In my code h=1/12, so we have error of 1/144.
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| Apr 5, 2021 at 10:20 | comment | added | Mariusz Iwaniuk |
For x=0 both methods yield 0.65741153600362792,but using method user @Ulrich Neumann give us 2/3.Which is correct one?
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| Apr 5, 2021 at 10:00 | history | answered | Alex Trounev | CC BY-SA 4.0 |