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Jun
30
awarded  Nice Question
Jun
23
comment How can I get Mathematica to produce better Fortran code?
Come on, not every one can spend another $2,495.00 without hesitation. BTW, the discount of MathCode for students is really stingy compared to Mathematica: Mathematica student version only sells for 140 dollars (50.00 dollars in China, at least when I bought it), while MathCode sells for $1,095.00 even in education store!
Jun
21
comment Smoothing a unit step function
After a second look I think your question is a little unclear. What do you really want? Smoothen n with NDSolve or find a smooth approximation of n which is to be used in NDSolve?
Jun
21
comment How to use NDSolve with discontinuities at internal boundaries?
@Dr.Know To deal with discontinuities of derivatives, you can try changing the independent variable, for example $f′(0+)/f′(0−)=\lambda$ can be "eliminated" by $ζ=c z$ where $c$ is a piecewise coefficient.
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
20
answered How to use NDSolve with discontinuities at internal boundaries?
Jun
20
revised How to use NDSolve with discontinuities at internal boundaries?
added 51 characters in body
Jun
13
reviewed Approve How expand Binomial[n, k] for k >= 6?
Jun
8
awarded  Nice Question
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
reviewed Approve In there a way to derive the inverse value of CDF format MultinormalDistribution?
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
awarded  Enlightened
Jun
3
awarded  Nice Answer
Jun
3
revised How to solve the differential equation with Duhamel's integral?
added 52 characters in body
Jun
3
revised How to solve the differential equation with Duhamel's integral?
added 7 characters in body
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.