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Jun
21
comment How to use NDSolve with discontinuities at internal boundaries?
One possible reason for the failure of the former approach is WhenEvent can only deal with IVP (at least now). (Just checked the document of WhenEvent and saw no example for a BVP. )
Jun
20
comment How to use NDSolve with discontinuities at internal boundaries?
Sadly this answer is wrong. Just compare the values at z=0 with OP's, they're apparently different.
Jun
5
comment Diverging solution to coupled second order ODEs from NDSolve
@AlbertRetey Very surprising! In this case changing 1.5 to 3/2 is necessary, or WorkingPrecision -> 32 won't work at all! I used to think that though the warning NDSolve::precw will be generated, as long as a higher WorkingPrecision is set, approximate numbers in the differential equation won't influence the result. (Actually I never saw this principle failed before!)
Jun
4
comment How to solve the differential equation with Duhamel's integral?
@MichaelE2 Er…sorry, but I just can't figure out how to calculate the n-th derivative at $t=0$ where $n>2$. $x''(0)$ can be obtained by Solve[eq /. t -> 0, x''[0]]/. x[0] -> 0 (* => x''[0] == 0.000625 *), but when it comes to D[eq, t], a $\frac{x'(0)}{\sqrt{t}}$ term involves in. One may argue that since $x'(0)=0$ so this term is (probably) zero at $t=0$, too, but when it comes to D[eq, {t, 2}], a $\frac{x''(0)}{\sqrt{t}}$ term involves in…
Jun
3
comment How to solve the differential equation with Duhamel's integral?
Oh, "Adding the dummy algebraic equation y[t] == y0[t] to the system helps with the accuracy." I missed this sentence, seems that I'm a little tired today 囧
Jun
3
comment How to solve the differential equation with Duhamel's integral?
As to the accuracy part: it's possible to improve the accuracy of FunctionInterpolation, see the edit of my answer.
Jun
3
comment How to solve the differential equation with Duhamel's integral?
Very interesting. BTW the dae = y[t] == y0[t]; line isn't necessary.
May
26
comment Solve wave equation using DSolve?
@kattern As to the The actual situation: is a solution involving unevaluated InverseLaplaceTransform acceptable?
May
26
comment Solve PDE with DiracDelta function
In v9.0.1, DSolve returns unevaluated after a warning. For the FourierTransform part: unlike LaplaceTransform, currently FourierTransform isn't handy. To circumvent this, here's a shell for enhancing. But what's really troublesome is: the ODE isn't defined in a infinite domain, so Fourier transform can't be used directly, theoretically one can extend the domain in cycles with e.g. Mod, but personally I never succeeded in the subsequent step: perhaps a artificial periodic function is too hard for FourierTransform, I'm not sure.
May
20
comment Save a C compiled function without losing the blessing of C compiler
@OleksandrR. Er…are you sure? I just tested the code in this answer, and funcNew apparently makes use of the DLL even if I restart Mathematica: i.stack.imgur.com/gIqig.png
May
19
comment Can Mathematica be used for developing “normal” stand-alone software?
Related: mathematica.stackexchange.com/q/37888/1871
May
19
comment Laplace transform of $\frac{1-\cos (t)}{t}$
Well, are you sure that LaplaceTransform[f[t], t, 2 s] is always equal to LaplaceTransform[f[t/2], t, s]?
May
16
comment Analogue for Maple's dchange - change of variables in differential expressions
How about adding one more syntax dChange[expresion, rule, {oldVars}, {newVars}, {functions}] that will internally make use of CoordinateTransform instead of Solve? Then one can do something like Assuming[{r > 0, -Pi < θ < Pi}, dChange[D[f[x, y], x, x] + D[f[x, y], y, y] == 0, "Cartesian" -> "Polar", {x, y}, {r, θ}, f[x, y]]]
May
13
comment Manipulating a damped oscillator plot - plot does not show
possible duplicate of Manipulate not showing anything
May
13
comment Bilateral Laplace Transform
@Guesswhoitis. Yeah, I know, but InverseFourierTransform doesn't know 囧:i.stack.imgur.com/PGcPh.png
May
12
comment Bilateral Laplace Transform
@jlperla I managed to make a better implementation of bilateral Laplace transform, it can handle DE now, have a look!
May
9
comment Save a C compiled function without losing the blessing of C compiler
Actually there's no need to use LibraryFunctionLoad, the only necessary part is to save the DLL to a non-temporary directory. Then one can save & load f2 and recover the C compiled function with something like f2new = ReplacePart[f2, {-1,1} -> (* The file path of the DLL *)]. In this way the RuntimeAttributes of the compiled function will also be recovered so your answer will be fully apply to this question :D
May
9
comment Save a C compiled function without losing the blessing of C compiler
+1. BTW it's a little surprising to me that the default Directory[] isn't included in $LibraryPath.
May
7
comment How to implement symbolic Ramanujan's summation in Mathematica?
@Anixx Yeah, the ability of Sum seems to become the new threshold. BTW the new formula using DifferenceDelta is even harder to implement… p.s. I suggest you to add these formulas to the question rather than in the comment only.
May
7
comment Speed up the auxiliary function magicSquare when $n$ is doubly-even
@ShutaoTang It's undocumented, but mentioned in a few posts here, for example this. You can have a search for more…Well, I admit I found no detailed explanation for so long. Maybe you can consider asking a separate question for this issue?