Robert Israel

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15 years, 332 days
University of British Columbia
Associate Professor Emeritus
North York, Ontario, Canada

MaplePrimes Activity


These are replies submitted by Robert Israel

@Christopher2222 : if the end of the rod at x=2 is "open", i.e. there is no heat flowing out of it (the convective cooling being along the sides of the rod), then the boundary condition at x=2 should be D[1](T)(2,t) = 0.

@Christopher2222 : if the end of the rod at x=2 is "open", i.e. there is no heat flowing out of it (the convective cooling being along the sides of the rod), then the boundary condition at x=2 should be D[1](T)(2,t) = 0.

It's not so clear that this body should cool down.  You do have loss of heat from radiation at the right endpoint, but you're keeping the temperature fixed at the left endpoint, so heat can enter there.  At equilibrium there will be a constant flow of heat and a constant temperature gradient.  It's not obvious whether that equilibrium will be above or below your initial temperatures.  It turns out to be slightly above.   That is, at equilibrium
T(x) = 1573 - k*x where lambda*k = sigma*epsilon*(T(L)^4 - T0^4).  I get
approximately k = 3845.84 which makes T(L) approximately 726.91, compared to your  T(L,0) = 685.  Maple 15 (using a smaller timestep) produces results consistent with this.

An exact expression for the period is T = 4*sqrt(L/g)*EllipticK(sin(theta/2)).

@rlopez : L is the list of coefficients produced by PolynomialTools:-CoefficientList, namely [0, 0, 0, 1/3, 1/12, 1/60, 1/360, 1/2520, 1/20160].
According to the information provided using infolevel, the actual work is done by listtodiffeq in the gfun package.  This looks for a linear differential equation with polynomial coefficients satisfied by the corresponding power series.  I presume this checks for linear dependencies of the form Sum(Sum(a[i,j]*x^i * (f^(``(j))),i),j)(up to some order in x)

Use display from the plots package to combine several plots.

Use display from the plots package to combine several plots.

@Alejandro Jakubi : if you do run the methods in parallel and several claim to find an answer, but those answers are all different, what do you do?  How can Maple know which answer is right?

@Alejandro Jakubi : if you do run the methods in parallel and several claim to find an answer, but those answers are all different, what do you do?  How can Maple know which answer is right?

Of course, what the Picard iteration is doing in this case is grinding out, one term at a time, the Maclaurin series of the solution.  That could be obtained more simply with dsolve(..., type=series)
As for guessgf, how does it come up with an answer?  Let's use infolevel[gfun] to get information on what it did.


> infolevel[gfun]:= 2;
 guessgf(L, x);

guessgf:   Trying to find a rational generating function
guessgf:   Trying to find an hypergeometric generating function
guessgf:   Trying to find an algebraic generating function
guessgf:   Trying to find a linear differential equation
listtodiffeq:   The   ogf   seems to satisfy   x^2+y(x)-diff(y(x),x)
guessgf:   Trying to solve it
                                     2
                        [-2 - 2 x - x  + 2 exp(x), ogf]


Surprise! It did it by solving the same differential equation we started with.

It looks like your listenouveau is an expression sequence, not a list.  Try [listenouveau] instead.

It looks like your listenouveau is an expression sequence, not a list.  Try [listenouveau] instead.

Do you mean you're getting that in the file as Excel displays it, or in the file name?  Neither of these happens for me.  What exactly did you do to get that result?

Do you mean you're getting that in the file as Excel displays it, or in the file name?  Neither of these happens for me.  What exactly did you do to get that result?

Yes, it seems something has changed on the server.  The code doesn't work in Maple 14 any more either, the Sockets:-Read call returning that HTTP error code.

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